MAT 540 Final Exam (20 Sets)

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MAT 540 Midterm Exam (5 Sets)

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MAT 540 Midterm Exam Set 1

Question 1 Deterministic techniques assume that no uncertainty exists in model parameters.

Question 2 A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.

Question 3 A continuous random variable may assume only integer values within a given interval.

Question 4 A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.

Question 5 Simulation results will always equal analytical results if 30 trials of the simulation have been conducted.

Question 6 Excel can only be used to simulate systems that can be represented by continuous random variables.

Question 7 Data cannot exhibit both trend and cyclical patterns.

Question 8 The Delphi develops a consensus forecast about what will occur in the future.

Question 9 In Bayesian analysis, additional information is used to alter the __________ probability of the occurrence of an event.

Question 10 __________ is a measure of dispersion of random variable values about the expected value.

Question 11 The __________ is the maximum amount a decision maker would pay for additional information.

Question 12 Developing the cumulative probability distribution helps to determine

Question 13 A seed value is a(n)

Question 14 Pseudorandom numbers exhibit __________ in order to be considered truly random.

Question 15 Consider the following frequency of demand:

If the simulation begins with 0.8102, the simulated value for demand would be

Question 16 __________ is a linear regression model relating demand to time.

Question 17 worth 2 points, 1 hour time limit (chapters 1,ue units EXCEPT:The U.S. Department of Agriculture estimates that the yearly yield of limes per acre is distributed as follows: Yield, bushels per acre Probability 350 .10 400 .18 450 .50 500 .22

The estimated average price per bushel is $16.80.

What is the expected yield of the crop?

Question 18 __________ methods are the most common type of forecasting method for the long-term strategic planning process.

Question 19 In exponential smoothing, the closer alpha is to __________, the greater the reaction to the most recent demand.

Question 20 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

If the forecast for period 5 is equal to 275, use exponential smoothing with Îą = .40 to compute a forecast for period 7.

Question 21

Question 22 Coefficient of determination is the percentage of the variation in the __________ variable that results from the __________ variable.

Question 23 Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors?

Question 24 Consider the following demand and forecast. Period Demand Forecast 1 7 10 2 12 15 3 18 20 4 22

If MAD = 2, what is the forecast for period 4?

Question 25 An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table or a graph, both shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints. xi 0 1 2 3 4 5 6 p(xi) .10 .15 .18 .20 .20 .10 .07

What is the average number of complaints received per week? Round your answer to two places after the decimal.

Question 26 An online sweepstakes has the following payoffs and probabilities. Each person is limited to one entry.

The probability of winning at least $1,000.00 is ________.

Question 27 A fair die is rolled 8 times. What is the probability that an even number (2,4, 6) will occur between 2 and 4 times? Round your answer to four places after the decimal.

Question 28 A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75? Round your answer to four places after the decimal.

Question 29 The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000).

If he uses the maximin criterion, how many new workers will he hire?

Question 30 An investor is considering 4 different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

Economic Condition Poor Average Good Excellent Investment (S1) (S2) (S3) (S4) A 50 75 20 30 B 80 15 40 50 C -100 300 -50 10 D 25 25 25 25

If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05 respectively, what is the highest expected payoff?

Question 31 A normal distribution has a mean of 500 and a standard deviation of 50. A manager wants to simulate one value from this distribution, and has drawn the number 1.4 randomly. What is the simulated value?

Question 32 Consider the following annual sales data for 2001-2008.

Calculate the correlation coefficient . Use four significant digits after the decimal.

Question 33 The following data summarizes the historical demand for a product.

Use exponential smoothing with Îą = .2 and the smoothed forecast for July is 32. Determine the smoothed forecast for August.

Question 34 Robert wants to know if there is a relation between money spent on gambling and winnings.

What is the coefficient of determination? Note: please report your answer with 2 places after the decimal point.

Question 35 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

Compute a 3-period moving average for period 6. Use two places after the decimal.

Question 36 Given the following data, compute the MAD for the forecast.

Question 37 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

Compute a 3-period moving average for period 4. Use two places after the decimal.

Question 38 The following sales data are available for 2003-2008 : Calculate the absolute value of the average error. Use three significant digits after the decimal.

Question 39 The following data summarizes the historical demand for a product

If the forecasted demand for June, July and August is 32, 38 and 42, respectively, what is MAPD? Write your answer in decimal form and not in percentages. For example, 15% should be written as 0.15. Use three significant digits after the decimal.

Question 40 This is the data from the last 4 weeks:

Use the equation of the regression line to forecast the increased sales for when the number of ads is 10.

MAT 540 Midterm Exam Set 2

Question 1 Deterministic techniques assume that no uncertainty exists in model parameters.

Question 2 A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.

Question 3 An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than 2 incorrect inspections is 0.736.

Question 4 A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.

Question 5 Starting conditions have no impact on the validity of a simulation model.

Question 6 Excel can only be used to simulate systems that can be represented by continuous random variables.

Question 7 Data cannot exhibit both trend and cyclical patterns.

Question 8 Qualitative methods are the least common type of forecasting method for the long-term strategic planning process.

Question 9 __________ is a measure of dispersion of random variable values about the expected value.

Question 10 In Bayesian analysis, additional information is used to alter the __________ probability of the occurrence of an event.

Question 11 The __________ is the expected value of the regret for each decision.

Question 12 Developing the cumulative probability distribution helps to determine

Question 13 A seed value is a(n)

Question 14 In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.

Question 15 Two hundred simulation runs were completed using the probability of a machine breakdown from the table below. The average number of breakdowns from the simulation trials was 1.93 with a standard deviation of 0.20.

Question 16 In exponential smoothing, the closer alpha is to __________, the greater the reaction to the most recent demand.

Question 17 __________ is absolute error as a percentage of demand.

Question 18 __________ is a category of statistical techniques that uses historical data to predict future behavior.

Question 19 Worth 2 points, 1 hour time limit (chapters 1,ue units EXCEPT:The U.S. Department of Agriculture estimates that the yearly yield of limes per acre is distributed as follows:

The estimated average price per bushel is $16.80.

What is the expected yield of the crop?

Question 20 __________ is a linear regression model relating demand to time.

Question 21 Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors?

Question 23 __________ is the difference between the forecast and actual demand.

Question 24 __________ methods are the most common type of forecasting method for the long-term strategic planning process.

Question 25 A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is larger than 21 oz? Round your answer to four places after the decimal.

Question 26 An online sweepstakes has the following payoffs and probabilities. Each person is limited to one entry.

The probability of winning at least $1,000.00 is ________.

Question 27 A fair die is rolled 8 times. What is the probability that an even number (2,4, 6) will occur between 2 and 4 times? Round your answer to four places after the decimal.

Question 28 A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75? Round your answer to four places after the decimal.

Question 29 An investor is considering 4 different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below. If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05 respectively, what is the highest expected payoff?

Question 30 The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000).

If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50% respectively, what is the expected value of perfect information? Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary.

Question 31 Given the following random number ranges and the following random number sequence: 62, 13, 25, 40, 86, 93, determine the average demand for the following distribution of demand.

Question 32 The following data summarizes the historical demand for a product

If the forecasted demand for June, July and August is 32, 38 and 42, respectively, what is MAPD? Write your answer in decimal form and not in percentages. For example, 15% should be written as 0.15. Use three significant digits after the decimal.

Question 33 The following data summarizes the historical demand for a product.

Use exponential smoothing with Îą = .2 and the smoothed forecast for July is 32. Determine the smoothed forecast for August.

Question 34 Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a 2 day moving average.

Question 35 Robert wants to know if there is a relation between money spent on gambling and winnings.

What is the coefficient of determination? Note: please report your answer with 2 places after the decimal point.

Question 36 This is the data from the last 4 weeks:

Use the equation of the regression line to forecast the increased sales for when the number of ads is 10.

Question 37 Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a weighted moving average, with weights of .6, .3 and .1, where the highest weights are applied to the most recent data.

Question 38 Given the following data, compute the MAD for the forecast.

Year

Demand

Forecast

Question 39 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

Compute a 3-period moving average for period 6. Use two places after the decimal.

Question 40 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

Compute a 3-period moving average for period 4. Use two places after the decimal.

MAT 540 Midterm Exam Set 3

Question 1 Deterministic techniques assume that no uncertainty exists in model parameters.

Question 2 An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than 2 incorrect inspections is 0.736.

Question 3 A continuous random variable may assume only integer values within a given interval.

Question 4 A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.

Question 5 Excel can only be used to simulate systems that can be represented by continuous random variables.

Question 6 A table of random numbers must be normally distributed and efficiently generated.

Question 7 The Delphi develops a consensus forecast about what will occur in the future.

Question 8 Data cannot exhibit both trend and cyclical patterns.

Question 9 In Bayesian analysis, additional information is used to alter the __________ probability of the occurrence of an event.

Question 10 __________ is a measure of dispersion of random variable values about the expected value.

Question 11 The __________ is the maximum amount a decision maker would pay for additional information.

Question 12 Pseudorandom numbers exhibit __________ in order to be considered truly random.

Question 13 Developing the cumulative probability distribution helps to determine

Question 14 Consider the following frequency of demand:

If the simulation begins with 0.8102, the simulated value for demand would be

Question 15 Random numbers generated by a __________ process instead of a __________ process are pseudorandom numbers.

Question 16 __________ is a category of statistical techniques that uses historical data to predict future behavior.

Question 17 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

If the forecast for period 5 is equal to 275, use exponential smoothing with Îą = .40 to compute a forecast for period 7.

Question 18 Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

Question 19 Consider the following demand and forecast.

Period Demand Forecast 1 7 10 2 12 15 3 18 20

4 22

If MAD = 2, what is the forecast for period 4?

Question 20 Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

Question 21 __________ methods are the most common type of forecasting method for the long-term strategic planning process.

What is the expected value at node 4? Round your answer to the nearest whole number. Do not include the dollar sign â€œ$â€? in your answer.

Question 31 A normal distribution has a mean of 500 and a standard deviation of Question 32 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

Compute a 3-period moving average for period 6. Use two places after the decimal.

Question 33 The following sales data are available for 2003-2008.

Determine a 4-year weighted moving average forecast for 2009, where weights are W1 = 0.1, W2 = 0.2, W3 = 0.2 and W4 = 0.5.

Question 34 The following data summarizes the historical demand for a product If the forecasted demand for June, July and August is 32, 38 and 42, respectively, what is MAPD? Write your answer in decimal form and not in percentages. For example, 15% should be written as 0.15. Use three significant digits after the decimal.

Question 35 Robert wants to know if there is a relation between money spent on gambling and winnings.

What is the coefficient of determination? Note: please report your answer with 2 places after the decimal point.

Question 36 Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a 2 day moving average.

Question 37 Consider the following annual sales data for 2001-2008.

Calculate the correlation coefficient . Use four significant digits after the decimal.

Question 38 Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a weighted moving average, with weights of .6, .3 and .1, where the highest weights are applied to the most recent data.

Question 39 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

Compute a 3-period moving average for period 4. Use two places after the decimal.

Question 40 Given the following data, compute the MAD for the forecast. MAT 540 Midterm Exam Set 4

Question 1 Deterministic techniques assume that no uncertainty exists in model parameters.

Question 2 An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than 2 incorrect inspections is 0.736.

Question 3 A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.

Question 5 Simulation results will always equal analytical results if 30 trials of the simulation have been conducted.

Question 6 A table of random numbers must be normally distributed and efficiently generated.

Question 7 The Delphi develops a consensus forecast about what will occur in the future.

Question 8 Data cannot exhibit both trend and cyclical patterns.

Question 9 Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What time is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot?

Question 10 In Bayesian analysis, additional information is used to alter the __________ probability of the occurrence of an event.

Question 11 The __________ is the expected value of the regret for each decision.

Question 12 Consider the following frequency of demand:

If the simulation begins with 0.8102, the simulated value for demand would be

Question 13 Pseudorandom numbers exhibit __________ in order to be considered truly random.

Question 14 Developing the cumulative probability distribution helps to determine

Question 15 A seed value is a(n)

Question 16 __________ is a measure of the strength of the relationship between independent and dependent variables.

Question 17 __________ is a linear regression model relating demand to time.

Question 18 Coefficient of determination is the percentage of the variation in the __________ variable that results from the __________ variable.

Question 19 __________ is the difference between the forecast and actual demand.

Question 20 Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

Question 21 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame: If the forecast for period 5 is equal to 275, use exponential smoothing with Îą = .40 to compute a forecast for period 7.

Question 22 worth 2 points, 1 hour time limit (chapters 1,ue units EXCEPT:The U.S. Department of Agriculture estimates that the yearly yield of limes per acre is distributed as follows:

Yield, bushels per acre Probability 350 .10 400 .18 450 .50 500 .22 The estimated average price per bushel is $16.80. What is the expected yield of the crop?

Question 23 __________ methods are the most common type of forecasting method for the long-term strategic planning process.

Question 24 __________ is a category of statistical techniques that uses historical data to predict future behavior.

Question 25 A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75? Round your answer to four places after the decimal.

Question 26 A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is larger than 21 oz? Round your answer to four places after the decimal.

Question 27 The drying rate in an industrial process is dependent on many factors and varies according to the following distribution. Compute the mean drying time. Use two places after the decimal.

Question 28 An online sweepstakes has the following payoffs and probabilities. Each person is limited to one entry.

The probability of winning at least $1,000.00 is ________.

Question 29 An investor is considering 4 different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05 respectively, what is the highest expected payoff?

Question 30 The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net

revenues will vary with how well taxpayers comply with the new tax code.

If he is conservative, how many new workers will he hire?

â€˘ Question 31 Consider the following distribution and random numbers:

If a simulation begins with the first random number, what would the first simulation value would be __________.

â€˘ Question 32 This is the data from the last 4 weeks:

Use the equation of the regression line to forecast the increased sales for when the number of ads is 10.

Question 33 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame: Compute a 3-period moving average for period 4. Use two places after the decimal.

Question 34 Given the following data, compute the MAD for the forecast.

Question 35 Consider the following annual sales data for 2001-2008. Calculate the correlation coefficient . Use four significant digits after the decimal.

Question 36 Robert wants to know if there is a relation between money spent on gambling and winnings. What is the coefficient of determination? Use two significant places after the decimal.

Question 37 The following data summarizes the historical demand for a product

If the forecasted demand for June, July and August is 32, 38 and 42, respectively, what is MAPD? Write your answer in decimal form and not in percentages. For example, 15% should be written as 0.15. Use three significant digits after the decimal.

Question 38 The following sales data are available for 2003-2008.

Determine a 4-year weighted moving average forecast for 2009, where weights are W1 = 0.1, W2 = 0.2, W3 = 0.2 and W4 = 0.5.

Question 39 Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a 2 day moving average.

Question 40 The following sales data are available for 2003-2008 :

Calculate the absolute value of the average error. Use three significant digits after the decimal.

MAT 540 Midterm Exam Set 5

Question 1 Deterministic techniques assume that no uncertainty exists in model parameters.

Question 2 A continuous random variable may assume only integer values within a given interval.

Question 3 A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.

Question 5 Excel can only be used to simulate systems that can be represented by continuous random variables.

Question 6 Starting conditions have no impact on the validity of a simulation model.

Question 7 Qualitative methods are the least common type of forecasting method for the long-term strategic planning process.

Question 8 Data cannot exhibit both trend and cyclical patterns.

Question 9 Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What time is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot?

Question 10 __________ is a measure of dispersion of random variable values about the expected value.

Question 11 The __________ is the expected value of the regret for each decision.

Question 12 Consider the following frequency of demand: If the simulation begins with 0.8102, the simulated value for demand would be

Question 13 Random numbers generated by a __________ process instead of a __________ process are pseudorandom numbers.

Question 14 Two hundred simulation runs were completed using the probability of a machine breakdown from the table below. The average number of breakdowns from the simulation trials was 1.93 with a standard deviation of 0.20. No. of breakdowns per week Probability Cumulative probability What is the probability of 2 or fewer breakdowns?

Question 15 Pseudorandom numbers exhibit __________ in order to be considered truly random.

Question 16 __________ is a category of statistical techniques that uses historical data to predict future behavior.

Question 17 __________ methods are the most common type of forecasting method for the long-term strategic planning process.

Question 18 __________ is a linear regression model relating demand to time.

Question 19 rob 14, and 15)estion worth 2 points, 1 hour time limit (chapters 1,ue units EXCEPT:The U.S. Department of Agriculture estimates that the yearly yield of limes per acre is distributed as follows: The estimated average price per bushel is $16.80. What is the expected yield of the crop?

Question 20 In exponential smoothing, the closer alpha is to __________, the greater the reaction to the most recent demand.

Question 21 __________ is absolute error as a percentage of demand.

Question 22 Consider the following graph of sales. Which of the following characteristics is exhibited by the data?

Question 23 Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors?

Question 24 Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time fram

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MAT 540 Week 1 Discussion Class Introductions

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www.tutorialrank.com "Class Introductions" Please respond to the following: Âˇ Please introduce yourself, including your educational and career goals, as well as some personal information about yourself. In your introduction, please draw from your own experience (or use a search engine) to give an example of how probability is used in your chosen profession. If you get your information from an online or other resource, be sure to cite the source of the information

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MAT 540 Week 1 Homework Chapter 1 and Chapter 11 (Solutions 100% Correct)

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www.tutorialrank.com MAT 540 Week 1 Homework Chapter 1

1. The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $65,000. The variable cost of recapping a tire is $7.5. The company charges$25 to recap a tire. a. For an annual volume of 15, 000 tire, determine the total cost, total revenue, and profit. b. Determine the annual break-even volume for the Retread Tire Company operation.

2. Evergreen Fertilizer Company produces fertilizer. The companyâ€™s fixed monthly cost is $25,000, and its variable cost per pound of fertilizer is $0.20. Evergreen sells the fertilizer for $0.45 per pound. Determine the monthly break-even volume for the company.

3. If Evergreen Fertilizer Company in problem 2 changes the price of its fertilizer from $0.45 per pound to $0.55 per pound, what effect will the change have on the break-even volume?

4. If Evergreen Fertilizer Company increases its advertising expenditure by $10,000 per year, what effect will the increase have on the break-even volume computed in problem 2?

5. Annie McCoy, a student at Tech, plans to open a hot dog stand inside Techâ€™s football stadium during home games. There are 6 home games scheduled for the upcoming season. She must pay the

Tech athletic department a vendorâ€™s fee of $3,000 for the season. Her stand and other equipment will cost her $3,500 for the season. She estimates that each hot dog she sells will cost her $0.40. she has talked to friends at other universities who sell hot dogs at games. Based on their information and the athletic departmentâ€™s forecast that each game will sell out, she anticipates that she will sell approximately 1,500 hot dogs during each game. a. What price should she charge for a hot dog in order to break even? b. What factors might occur during the season that would alter the volume sold and thus the break-even price Annie might charge?

6. The college of business at Kerouac University is planning to begin an online MBA program. The initial start-up cost for computing equipment, facilities, course development and staff recruitment and development is $400,000. The college plans to charge tuition of $20,000 per student per year. However, the university administration will charge the college $10,000 per student for the first 100

students enrolled each year for administrative costs and its share of the tuition payments. a. How many students does the college need to enroll in the first year to break-even? b. If the college can enroll 80 students the first year, how much profit will it make? MAT540 Homework

c. The college believes it can increase tuition to $25,000, but doing so would reduce enrollment to 50. Should the college consider doing this?

7. The following probabilities for grades in management science have been determined based on past records: Grade Probability A 0.1 B 0.2

C 0.4 D 0.2 F 0.10 1.00 The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine the expected grade and variance for the course.

8. An investment firm is considering two alternative investments, A and B, under two possible future sets of economic conditions good and poor. There is a .60 probability of good economic conditions occurring and a .40 probability of poor economic conditions occurring. The expected gains and losses under each economic type of conditions are shown in the following table: Investment Economic Conditions Good Poor A $380,000 -$100,000 B $130,000 $85,000

Using the expected value of each investment alternative, determine which should be selected.

9. The weight of the bags of fertilizer is normally distributed, with a mean of 45 pounds and a standard deviation of 5 pounds. What is the probability that a bag of fertilizer will weigh between 38 and 50 pounds

10. The polo Development Firm is building a shopping center. It has informed renters that their rental spaces will be ready for occupancy in 18 months. If the expected time until the shopping center is completed is estimated to be 15 months, with a standard deviation of 5 months, what is the probability that the renters will not be able to occupy in 18 months?

11. The manager of the local National Video Store sells videocassette recorders at discount prices. If

the store does not have a video recorder in stock when a customer wants to buy one, it will lose the sale because the customer will purchase a recorder from one of the many local competitors. The problem is that the cost of renting warehouse space to keep enough recorders in inventory to meet all demand is excessively high. The manager has determined that if 85% of customer demand for recorders can be met, then the combined cost of lost sales and inventory will be minimized. The manager has estimated that monthly demand for recorders is normally distributed, with a mean of 175 recorders and a standard deviation of 55. Determine the number of recorders the manager should order each month to meet 85% of customer demand.

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MAT 540 Week 1-10 All Homework

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www.tutorialrank.com MAT 540 Week 1 Homework Chapter 1 and Chapter 11

MAT 540 Week 2 Homework Chapter 12

MAT 540 Week 3 Homework Chapter 14

MAT 540 Week 4 Homework Chapter 15

MAT 540 Week 6 Homework Chapter 2

MAT 540 Week 7 Homework Chapter 3

MAT 540 Week 8 Homework Chapter 4

MAT 540 Week 9 Homework Chapter 5

MAT 540 Week 10 Homework Chapter 6

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MAT 540 Week 1-11 All Discussion Question

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www.tutorialrank.com MAT 540 Week 1 Discussion Class Introductions

MAT 540 Week 2 Discussion Expected value of perfect information

MAT 540 Week 3 Discussion Simulation

MAT 540 Week 4 Discussion Forecasting Methods

MAT 540 Week 5 Discussion Reflection

MAT 540 Week 6 Discussion LP Models

MAT 540 Week 7 Discussion sensitivity analysis

MAT 540 Week 8 Discussion Practice setting up linear programming models for business applications

MAT 540 Week 9 Discussion Application of Integer Programming

MAT 540 Week 10 Discussion Transshipment problems

MAT 540 Week 11 Discussion Reflection to Date

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MAT 540 Week 1-11 All Homework, DQs, Midterm (5 Set) , Final Exam (20 Set)

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www.tutorialrank.com MAT 540 Midterm Exam (5 Sets)

MAT 540 Final Exam (20 Sets)

MAT 540 Week 1 Homework Chapter 1 and Chapter 11

MAT 540 Week 2 Homework Chapter 12

MAT 540 Week 3 Homework Chapter 14

MAT 540 Week 4 Homework Chapter 15

MAT 540 Week 6 Homework Chapter 2

MAT 540 Week 7 Homework Chapter 3

MAT 540 Week 8 Homework Chapter 4

MAT 540 Week 9 Homework Chapter 5

MAT 540 Week 10 Homework Chapter 6

MAT 540 Week 1 Discussion Class Introductions

MAT 540 Week 2 Discussion Expected value of perfect information

MAT 540 Week 3 Discussion Simulation

MAT 540 Week 4 Discussion Forecasting Methods

MAT 540 Week 5 Discussion Reflection

MAT 540 Week 6 Discussion LP Models

MAT 540 Week 7 Discussion sensitivity analysis

MAT 540 Week 8 Discussion Practice setting up linear programming models for business applications

MAT 540 Week 9 Discussion Application of Integer Programming

MAT 540 Week 10 Discussion Transshipment problems

MAT 540 Week 11 Discussion Reflection to Date

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MAT 540 Week 2 Discussion Expected value of perfect information

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www.tutorialrank.com In your own words, explain how to obtain the â€œexpected value of perfect informationâ€? for any payoff table, which has probabilities associated with each state of nature. Then, provide an example, drawing from any of the payoff tables in Problems 1-17 in the back of Chapter 12. If no probabilities are given for the states of nature, then assume equal likelihood. ===============================================

MAT 540 Week 2 Homework Chapter 12

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Week 2 Homework

Chapter 12

1. A local real estate investor in Orlando is considering three alternative investments; a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment:

Determine the best investment, using the following decision criteria.

a. Maximax

b. Maximin

c. Minimax regret

d. Hurwicz (Îą = 0.4)

e. Equal likelihood

2. A concessions manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is a 35% chance of rain, a 25% chance of overcast skies, and a 40% chance of sunshine, according to the weather forecast in college junction, where the game is to be held. The manager estimates that the following profits will result from each decision, given each set of weather conditions:

a. Compute the expected value for each decision and select the best one.

b. Develop the opportunity loss table and compute the expected opportunity loss for each decision.

3. Place-Plus, a real estate development firm, is considering several alternative development projects. These include building and leasing an office park, purchasing a parcel of land and building an office building to rent, buying and leasing a warehouse, building a strip mall, and selling condominiums. The financial success of these projects depends

on interest rate movement in the next 5 years. The various development projects and their 5- year financial return (in $1,000,000s) given that interest rates will decline, remain stable, or increase, are in the following payoff table. Place-Plus real estate development firm has hired an economist to assign a probability to each direction interest rates may take over the next 5 years. The economist has determined that there is a

0.45 probability that interest rates will decline, a 0.35 probability that rates will remain stable, and a

0.2 probability that rates will increase.

a. Using expected value, determine the best project.

b. Determine the expected value of perfect information.

4. The director of career advising at Orange Community College wants to use decision analysis to provide information to help students decide which 2-year degree program they should pursue. The director has set up the following payoff table for six of the most popular and successful degree programs at OCC that shows the estimated 5-Year gross income ($) from each degree for four future economic conditions:

Determine the best degree program in terms of projected income, using the following decision criteria:

a. Maximax

b. Maximin

c. Equal likelihood

d. Hurwicz (Îą=0.4)

5. Construct a decision tree for the following decision situation and indicate the best decision.

Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership. They have three offers: from a foreign compact car company, from a U.S. producer of full-sized cars, and from a truck company. The success of each type of dealership will depend on how much gasoline is going to be available during the next few years. The profit from each type of dealership, given the availability of gas, is shown in the following payoff table:

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MAT 540 Week 2 Quiz 1 (3 Sets)

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www.tutorialrank.com MAT 540 Week 2 Quiz 1 Set 1 QUESTIONS Question 1: Parameters are known, constant values that are usually coefficients of variables in equations. Question 2: If variable costs increase, but price and fixed costs are held constant, the break even point will decrease. Question 3: Probabilistic techniques assume that no uncertainty exists in model parameters. Question 4: Fixed cost is the difference between total cost and total variable cost. Question 5: A binomial probability distribution indicates the probability of r successes in n trials. Question 6: The events in an experiment are mutually exclusive if only one can occur at a time. Question 7: If events A and B are independent, then P(A|B) = P(B|A).

Question 8: If fixed costs increase, but variable cost and price remain the same, the break even point Question 9: If the price increases but fixed and variable costs do not change, the break even point Question 10: A bed and breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $4200 per month and the revenue they receive from each booked room is $180. What their variable cost per occupied room? Question 11: EKA manufacturing company produces Part # 2206 for the aerospace industry. Each unit of part # 2206 is sold for $15. The unit production cost of part # 2206 is $3. The fixed monthly cost of operating the production facility is $3000. How many units of part # 2206 have to be sold in a month to break-even? Question 12: In a binomial distribution, for each of n trials, the event Question 13: The expected value of the standard normal distribution is equal to Question 14: The area under the normal curve represents probability, and the total area under the curve sums to Question 15: Administrators at a university are planning to offer a summer seminar. The costs of reserving a room, hiring an instructor, and bringing in the equipment amount to $3000. Suppose that it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? Note: please report the result as a whole number, rounding if necessary and omitting the decimal point.

Question 16: A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45. Find the break-even point. Question 17: Administrators at a university will charge students $158 to attend a seminar. It costs $2160 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $50 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?Note: please report the result as a whole number, omitting the decimal point. Question 18: Wei is considering pursuing an MS in Information Systems degree. She has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Wei will be accepted by at least one of the two universities? {Express your answer as a percent. Round (if necessary) to the nearest whole percent and omit the decimal. For instance, 20.1% would be written as 20} Question 19: An inspector correctly identifies defective products 90% of the time. For the next 10 products, what is the probability that he makes fewer than 2 incorrect inspections?Note: Please report your answer with two places to the right of the decimal, rounding if appropriate. Question 20: An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table (shown below). The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

xi 0 1 2 3 4 5 6 p(xi) .10 .15 .18 .20 .20 .10 .07

What is the average number of complaints received per week? Note: Please report your answer with two places to the right of the decimal, rounding if appropriate.

MAT 540 Week 2 Quiz 1 Set 2 QUESTIONS Question 1 Probabilistic techniques assume that no uncertainty exists in model parameters. Question 2 Fixed cost is the difference between total cost and total variable cost. Question 3 If variable costs increase, but price and fixed costs are held constant, the break even point will decrease. Question 4 Parameters are known, constant values that are usually coefficients of variables in equations. Question 5 If events A and B are independent, then P(A|B) = P(B|A). Question 6 A continuous random variable may assume only integer values within a given interval. Question 7 The events in an experiment are mutually exclusive if only one can occur at a time. Question 8 If fixed costs increase, but variable cost and price remain the same, the break even point

Question 9 If the price increases but fixed and variable costs do not change, the break even point Question 10 The indicator that results in total revenues being equal to total cost is called the Question 11 A model is a functional relationship that includes: Question 12 In a binomial distribution, for each of n trials, the event Question 13 The area under the normal curve represents probability, and the total area under the curve sums to Question 14 The expected value of the standard normal distribution is equal to Question 15 Administrators at a university will charge students $158 to attend a seminar. It costs $2160 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $50 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even? Note: please report the result as a whole number, omitting the decimal point. Question 16 A production run of toothpaste requires a fixed cost of $100,000. The variable cost per unit is $3.00. If 50,000 units of toothpaste will be sold during the next month, what sale price must be chosen in order to break even at the end of the month? Note: please report the result as a whole number, rounding if necessary and omitting the decimal point. Question 17 Administrators at a university are planning to offer a summer seminar. The costs of reserving a room, hiring an instructor, and bringing in the equipment amount to $3000.

Suppose that it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? Note: please report the result as a whole number, rounding if necessary and omitting the decimal point. Question 18 The variance of the standard normal distribution is equal to __________. Question 19 Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

Male (M) Female (F) Job Administrative (AD)

110

10

Salaried staff (SS)

30

50

Hourly staff (HS)

60

40

If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration? Question 20 An inspector correctly identifies defective products 90% of the time. For the next 10 products, what is the probability that he makes fewer than 2 incorrect inspections? Note: Please report your answer with two places to the right of the decimal, rounding if appropriate.

MAT 540 Week 2 Quiz 1 Set 3 QUESTIONS Question 1 Parameters are known, constant values that are usually coefficients of variables in equations. Question 2 In general, an increase in price increases the break even point if all costs are held constant. Question 3 If variable costs increase, but price and fixed costs are held constant, the break even point will decrease. Question 4 Probabilistic techniques assume that no uncertainty exists in model parameters. Question 5 If events A and B are independent, then P(A|B) = P(B|A). Question 6 The events in an experiment are mutually exclusive if only one can occur at a time. Question 7 A binomial probability distribution indicates the probability of r successes in n trials. Question 8 A model is a functional relationship that includes: Question 9 If the price increases but fixed and variable costs do not change, the break even point Question 10 If fixed costs increase, but variable cost and price remain the same, the break even point Question 11 A bed and breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $4200 per month and the revenue they receive from each booked room is $180. What their variable cost per occupied room? Question 12 The expected value of the standard normal distribution is equal to

Question 13 In a binomial distribution, for each of n trials, the event Question 14 The area under the normal curve represents probability, and the total area under the curve sums to Question 15 A production run of toothpaste requires a fixed cost of $100,000. The variable cost per unit is $3.00. If 50,000 units of toothpaste will be sold during the next month, what sale price must be chosen in order to break even at the end of the month? Note: please report the result as a whole number, rounding if necessary and omitting the decimal point. Question 16 Administrators at a university are planning to offer a summer seminar. The costs of reserving a room, hiring an instructor, and bringing in the equipment amount to $3000. Suppose that it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? Note: please report the result as a whole number, rounding if necessary and omitting the decimal point. Question 17 A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45. Find the break-even point. Question 18 Wei is considering pursuing an MS in Information Systems degree. She has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Wei will be accepted by at least one of the two universities? {Express your answer as a percent. Round (if necessary) to the nearest whole percent and omit the decimal. For instance, 20.1% would be written as 20}

Question 19 The variance of the standard normal distribution is equal to __________.

Question 20 An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table (shown below). The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

xi 0 1 2 3 4 5 6 p(xi) .10 .15 .18 .20 .20 .10 .07

What is the average number of complaints received per week? Note: Please report your answer with two places to the right of the decimal, rounding if appropriate.

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MAT 540 Week 3 Discussion Simulation

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www.tutorialrank.com Select one (1) of the following topics for your primary discussion posting:

Identify the part of setting up a simulation in Excel that you find to be the most challenging, and explain why.

Identify resources that can help you with that. Explain how simulation is used in the real world.

Provide a specific example from your own line of work, or a line of work that you find particularly interesting.

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MAT 540 Week 3 Homework Chapter 14

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MAT 540 Week 3 Homework Chapter 14

1. The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following probability distribution. The squad is on duty 24 hours per day, 7 days per week: Time Between

a. Simulate the emergency calls for 3 days (note that this will require a â€œrunningâ€? , or cumulative, hourly clock), using the random number table. b. Compute the average time between calls and compare this value with the expected value of the time between calls from the probability distribution. Why are the result different?

2. The time between arrivals of cars at the Petroco Services Station is defined by the following probability distribution: Time Between

a. Simulate the arrival of cars at the service station for 20 arrivals and compute the average time between arrivals. b. Simulate the arrival of cars at the service station for 1 hour, using a different stream of random numbers from those used in (a) and compute the average time between arrivals. c. Compare the results obtained in (a) and (b). 3. The Dynaco Manufacturing Company produces a product in a process consisting of operations of five machines. The probability distribution of the number of machines that will break down in a week follows:

a. Simulate the machine breakdowns per week for 20 weeks. b. Compute the average number of machines that will break down per week.

4. Simulate the following decision situation for 20 weeks, and recommend the best decision.

A concessions manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather forecast in college junction, where the game is to be held. The manager estimates that the following profits will result from each decision, given each set of weather conditions: MAT540 Homework

5. Every time a machine breaks down at the Dynaco Manufacturing Company (Problem 3), either 1, 2, or 3 hours are required to fix it, according to the following probability distribution: Repair Time (hr.) Probability

Simulate the repair time for 20 weeks and then compute the average weekly repair time.

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MAT 540 Week 3 Quiz 2 (Two Sets)

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www.tutorialrank.com MAT 540 Week 3 Quiz 2 Set 1 QUESTIONS Question 1 If two events are not mutually exclusive, then P(A or B) = P(A) + P(B) Question 2 Probability trees are used only to compute conditional probabilities. Question 3 Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed. Question 4 Both maximin and minimin criteria are optimistic. Question 5 The equal likelihood criterion assigns a probability of 0.5 to each state of nature, regardless of how many states of nature there are. Question 6 The Hurwicz criterion is a compromise between the minimax and minimin criteria. Question 7 Using the minimax regret criterion, we first construct a table of regrets. Subsequently, for each possible decision, we look across the states of nature and make a note of the maximum regret possible for that decision. We then pick the decision with the largest maximum regret.

Question 8 Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot. Question 9 The chi-square test is a statistical test to see if an observed data fit a _________. Question 10 The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels? Question 11 A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

Weather Cold S1

Warm Rainy S2

S3

Bike: A1

10

8

6

Hike: A2

14

15

2

Fish: A3

7

8

9

What is the conservative decision for this situation? Question 12 A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. The maximin strategy is: Question 12 The maximin criterion results in the Question 13 A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is: Question 14 A brand of television has a lifetime that is normally distributed with a mean of 7 years and a standard deviation of 2.5 years. What is the probability that a randomly chosen TV will last more than 8 years? Note: Write your answers with two places after the decimal, rounding off as appropriate. Question 15 A life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 71 years and a standard deviation of 3.5 years. What proportion of the plan participants are expected to see their 75th birthday? Note: Write your answers with two places after the decimal, rounding off as appropriate. Question 16 A manager has developed a payoff table that indicates the profits associated with a set of alternatives under 2 possible states of nature.

Alt

S1

S2

1

10

2

2

-2

8

3

8

5

What is the highest expected value? Assume that the probability of S2 is equal to 0.4. Question 17 Consider the following decision tree. What is the expected value for the best decision? Round your answer to the nearest whole number. Question 18 A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. Question 19 If the probability of brisk business is .40, what is the numerical maximum expected value? Question 20 The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze (a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chance that the lot is fair quality (s2) and 20% chance that the lot is good quality (s3). What is the numerical value of the maximin? MAT 540 Week 3 Quiz 2 Set 2 QUESTIONS

Question 1 If two events are not mutually exclusive, then P(A or B) = P(A) + P(B) Question 2 Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed. Question 3 Probability trees are used only to compute conditional probabilities. Question 4 Using the minimax regret criterion, we first construct a table of regrets. Subsequently, for each possible decision, we look across the states of nature and make a note of the maximum regret possible for that decision. We then pick the decision with the largest maximum regret. Question 5 The maximin approach involves choosing the alternative with the highest or lowest payoff. Question 6 The Hurwicz criterion is a compromise between the minimax and minimin criteria. Question 7 The Hurwicz criterion is a compromise between the maximax and maximin criteria. Question 8 Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot. Question 9 A professor would like to utilize the normal distribution to assign grades such that 5% of students receive A's. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.

Question 10 The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels? Question 11 Determining the worst payoff for each alternative and choosing the alternative with the best worst is called Question 12 A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. The maximin strategy is: Question 13 A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is Question 14 The maximin criterion results in the Question 15 A life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 71 years and a standard deviation of 3.5 years. What proportion of the plan participants are expected to see their 75th birthday? Note: Write your answers with two places after the decimal, rounding off as appropriate.

Question 16 A brand of television has a lifetime that is normally distributed with a mean of 7 years and a standard deviation of 2.5 years. What is the probability that a randomly chosen TV will last more than 8 years? Note: Write your answers with two places after the decimal, rounding off as appropriate. Question 16 A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. Question 17 If the probability of brisk business is .40, what is the numerical maximum expected value? Question 18 A manager has developed a payoff table that indicates the profits associated with a set of alternatives under 2 possible states of nature.

Alt

S1

S2

1

10

2

2

-2

8

3

8

5

Compute the expected value of perfect information assuming that the probability of S2 is equal to 0.4. Question 19 A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

Weather Cold S1

Warm Rainy S2

S3

Bike: A1

10

8

6

Hike: A2

14

15

2

Fish: A3

7

8

9

Question 20 If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively what is the EVPI for this situation? Consider the following decision tree. What is the expected value for the best decision? Round your answer to the nearest whole number.

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MAT 540 Week 4 Discussion Forecasting Methods

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Discuss Forecasting Methods Select one (1) of the following topics for your primary discussion posting: â€˘ Identify any challenges you have in setting up a time-series analysis in Excel. Explain what they are and why they are challenging. Identify resources that can help you with that. â€˘ Explain how forecasting is used in the real world. Provide a specific example from your own line of work, or a line of work that you find particularly interesting.

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MAT 540 Week 4 Homework Chapter 15

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1. The manager of the Carpet City outlet needs to make an accurate forecast of the demand for Soft Shag carpet (its biggest seller). If the manager does not order enough carpet from the carpet mill, customer will buy their carpet from one of Carpet Cityâ€™s many competitors. The manager has collected the following demand data for the past 8 months: Compute a 3-month moving average forecast for months 4 through 9.

a. Compute a weighted 3-month moving average forecast for months 4 through 9. Assign weights of 0.55, 0.35, and 0.10 to the months in sequence, starting with the most recent month.

b. Compare the two forecasts by using MAD. Which forecast appears to be more accurate?

2. The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 10 months:

a. Compute an exponential smoothed forecast, using an Îą value of 0.4

b. Compute the MAD.

3. Emily Andrews has invested in a science and technology mutual fund. Now she is considering liquidating and investing in another fund. She would like to forecast the price of the science and technology fund for the next month before making a decision. She has collected the following data on the average price of the fund during the past 20 months:

a. Using a 3-month average, forecast the fund price for month 21.

b. Using a 3-month weighted average with the most recent month weighted 0.5, the next most recent month weighted 0.30, and the third month weighted 0.20, forecast the fund price for month 21.

c. Compute an exponentially smoothed forecast, using Îą=0.3, and forecast the fund price for month 21.

d. Compare the forecasts in (a), (b), and (c), using MAD, and indicate the most accurate.

4. Carpet City wants to develop a means to forecast its carpet sales. The store manager believes that the storeâ€™s sales are directly related to the number of new housing starts in town. The manager has gathered data from county records on monthly house construction permits and from store records on monthly sales. These data are as follows:

Monthly Carpet Sales Monthly Construction (1,000 yd.) Permits

9 17 14 25 10 8 12 7 15 14 97 24 45 21 19 20 28

a. Develop a linear regression model for these data and forecast carpet sales if 30 construction permits for new homes are filed.

b. Determine the strength of the causal relationship between monthly sales and new home construction by using correlation.

5. The manager of Gilleyâ€™s Ice Cream Parlor needs an accurate forecast of the demand for ice cream.

The store orders ice cream from a distributor a week ahead; if the store orders too little, it loses business, and if it orders too much, the extra must be thrown away. The manager belives that a major determinant of ice cream sales is temperature (i.e.,the hotter the weather, the more ice cream people buy). Using an almanac, the manager has determined the average day time temperature for 14 weeks, selected at random, and from store records he has determined the ice cream consumption for the same 14 weeks. These data are summarized as follows:

a. Develop a linear regression model for these data and forecast the ice cream consumption if the average weekly daytime temperature is expected to be 85 degrees.

b. Determine the strength of the linear relationship between temperature and ice cream consumption by using correlation.

c. What is the coefficient of determination? Explain its meaning.

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MAT 540 Week 5 Discussion Reflection

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MAT 540 Week 6 Discussion LP Models

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Discuss LP Models Select one (1) of the following topics for your primary discussion posting: â€˘ The objective function always includes all of the decision variables, but that is not necessarily true of the constraints. Explain the difference between the objective function and the constraints. Then, explain why a constraint need not refer to all the variables. â€˘ Pick any constraint from any problem in the text, and explain how to plot the line that corresponds to that constraint.

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MAT 540 Week 6 Homework Chapter 2

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1. A Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice,

provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 45 milligrams of vitamin A and 13 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 10 milligrams of vitamin A and 2 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 3 milligrams of B. An ounce of oats costs $0.06, and an ounce of rice costs $0.03. a. Formulate a linear programming model for this problem. b. Solve the model by using graphical analysis.

2. A Furniture Company produces chairs and tables from two resourceslabor and wood. The company has 125 hours of labor and 45 board-ft. of wood available each day. Demand for chairs is limited to 5 per day. Each chair requires 7 hours of labor and 3.5 boardft. of wood, whereas a table requires 14 hours of labor and 7 board-ft. of wood. The profit derived from each chair is $325 and from each table, $120. The company wants to determine the number of chairs and tables to produce

each day in order to maximize profit. Formulate a linear programming model for this problem. a. Formulate a linear programming model for this problem. b. Solve the model by using graphical analysis. (Do not round the answers) c. How much labor and wood will be unused if the optimal numbers of chairs and tables are produced?

3. Kroeger supermarket sells its own brand of canned peas as well as several national brands. The store makes a profit of $0.28 per can for its own peas and a profit of $0.19 for any of the national brands. The store has 6 square feet of shelf space available for canned peas, and each can of peas takes up 9 square inches of that space. Point-of-sale records show that each week the store never sales more than half as many cans of its own brand as it does of the national brands. The store wants to know how many cans of its own brand of peas of peas and how many cans of the national brands to stock each week on the allocated shelf space in order to maximize profit.

a. Formulate a linear programming model for this problem. b. Solve the model by using graphical analysis. MAT540 Homework

4. Solve the following linear programming model graphically: Minimize Z=8X1 + 6X2

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MAT 540 Week 7 Discussion sensitivity analysis

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www.tutorialrank.com Discuss sensitivity analysis Select one (1) of the following topics for your primary discussion posting:

â€˘ Identify any challenges you have in setting up a linear programming problem in Excel, and solving it with Solver. Explain exactly what the challenges are and why they are challenging. Identify resources that can help you with that. â€˘ Explain what the shadow price means in a maximization problem. Explain what this tells us from a management perspective.

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MAT 540 Week 7 Homework Chapter 3

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1. Southern Sporting Good Company makes basketballs and footballs. Each product is produced from two resources rubber and leather. Each basketball produced results in a profit of $11 and each football earns $15 in profit. The resource requirements for each product and the total resources

available are as follows: Product

Total resources available 600 900 a. Find the optimal solution. b. What would be the effect on the optimal solution if the profit for the basketball changed from $11 to $12? c. What would be the effect on optimal solution if 400 additional pounds of rubber could be obtained? What would be the effect if 600 additional square feet of leather could be obtained?

2. A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows: Product Resource Requirements per Unit Line 1 Line 2

A 11 5 B69 Total Hours 65 40

a. Formulate a linear programming model to determine the optimal product mix that will maximize profit.

b. What are the sensitivity ranges for the objective function coefficients? c. Determine the shadow prices for additional hours of production time on line 1 and line 2 and indicate whether the company would prefer additional line 1 or line 2 hours.

3. Formulate and solve the model for the following problem: Irwin Textile Mills produces two types of cotton cloth denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 8 pounds of raw cotton per yard, whereas denim requires 6 pounds of raw cotton per yard. A yard of corduroy requires 4 hours of processing time;

a yard od denim requires 3.0 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 510 yards per month. The manufacturer has 6,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $2.5 per yards of denim and $3.25 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. Formulate the model and put it into standard form. Solve it a. How much extra cotton and processing time are left over at the optimal solution? Is the demand for corduroy met? b. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer.

4. The Bradley family owns 410 acres of farmland in North Carolina on which they grow corn and tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest; each acre of tobacco costs

$210. The Bradleys’ have a budget of $52,500 for next year. The government limits the number of acres of tobacco that can be planted to 100. The profit from each acre of corn is $300; the profit from each acre of tobacco is $520. The Bradleys’ want to know how many acres of each crop to plant in order to maximize their profit.

a. Formulate the linear programming model for the problem and solve.

b. How many acres of farmland will not be cultivated at the optimal solution? Do the Bradleys use the entire 100-acre tobacco allotment?

c. The Bradleys’ have an opportunity to lease some extra land from a neighbor. The neighbor is offering the land to them for $110 per acre. Should the Bradleys’ lease the land at that price? What is the maximum price the Bradleys’ should pay their neighbor for the land, and how much land should they lease at that price? MAT540 Homework

d. The Bradleysâ€™ are considering taking out a loan to increase their budget. For each dollar they borrow, how much additional profit would they make? If they borrowed an additional $1,000, would the number of acres of corn and tobacco they plant change?

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MAT 540 Week 7 Quiz 3 (Three Sets)

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www.tutorialrank.com MAT 540 Week 7 Quiz 3 Set 1 QUESTIONS Question 1: Graphical solutions to linear programming problems have an infinite number of possible objective function lines. Question 2: The following inequality represents a resource constraint for a maximization problem: X + Y â‰Ľ 20

Question 3: In minimization LP problems the feasible region is always below the resource constraints. Question 4: In a linear programming problem, all model parameters are assumed to be known with certainty. Question 5: A feasible solution violates at least one of the constraints. Question 6: If the objective function is parallel to a constraint, the constraint is infeasible. Question 7: If the objective function is parallel to a constraint, the constraint is infeasible. Question 8: Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit? Question 9: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. Which of the following points are not feasible? Question 10: The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are

$3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint? Question 11: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. The equation for constraint DH is: Question 12: Which of the following statements is not true? Question 13: In a linear programming problem, a valid objective function can be represented as Question 14: The linear programming problem: MIN Z =

2x1 + 3x2

Subject to:

x1 + 2x2 ≤ 20 5x1 + x2 ≤ 40 4x1 +6x2 ≤ 60 x1 , x2 ≥ 0 ,

Question 15: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. This linear programming problem is a: Question 16: A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. If this is maximization, which extreme point is the optimal solution?

Question 17: Which of the following could be a linear programming objective function? Question 18: Solve the following graphically Max z =

3x1 +4x2

s.t.

x1 + 2x2 ≤ 16 2x1 + 3x2 ≤ 18 x1

≥2

x2

≤ 10

x1, x2 ≥ 0 Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 Question 19: Consider the following linear programming problem: Max Z =

$15x + $20y

Subject to:

8x + 5y ≤ 40 0.4x + y ≥ 4 x, y ≥ 0

At the optimal solution, what is the amount of slack associated with the first constraint? Question 20: Max Z = Subject to:

$3x + $9y

20x + 32y ≤ 1600

4x + 2y ≤ 240 y ≤ 40 x, y ≥ 0 At the optimal solution, what is the amount of slack associated with the second constraint?

MAT 540 Week 7 Quiz 3 Set 2 QUESTIONS Question 1: A linear programming problem may have more than one set of solutions. Question 2: A feasible solution violates at least one of the constraints. Question 3: Graphical solutions to linear programming problems have an infinite number of possible objective function lines. Question 4: In a linear programming problem, all model parameters are assumed to be known with certainty. Question 5: Surplus variables are only associated with minimization problems. Question 6: A linear programming model consists of only decision variables and constraints. Question 7: If the objective function is parallel to a constraint, the constraint is infeasible. Question 8: Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to

invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit? Question 9: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. This linear programming problem is a: Question 10: Decision variables Question 11: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. Which of the following points are not feasible? Question 12: Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the objective function? Question 13: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. The equation for constraint DH is: Question 14: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.

Which of the following constraints has a surplus greater than 0? Question 15: A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. If this is maximization, which extreme point is the optimal solution? Question 16: The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the objective function? Question 17: Which of the following could be a linear programming objective function? Question 18: A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your answer in decimal notation. Question 19: Max Z = Subject to:

$3x + $9y

20x + 32y ≤ 1600 4x + 2y ≤ 240 y ≤ 40

x, y ≥ 0 At the optimal solution, what is the amount of slack associated with the second constraint? Question 20: Solve the following graphically Max z =

3x1 +4x2

s.t.

x1 + 2x2 ≤ 16 2x1 + 3x2 ≤ 18 x1

≥2

x2

≤ 10

x1, x2 ≥ 0

Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 MAT 540 Week 7 Quiz 3 Set 3 QUESTIONS Question 1: A feasible solution violates at least one of the constraints. Question 2: A linear programming model consists of only decision variables and constraints.

Question 3: If the objective function is parallel to a constraint, the constraint is infeasible.

Question 4: In minimization LP problems the feasible region is always below the resource constraints. Question 5: Surplus variables are only associated with minimization problems. Question 6: If the objective function is parallel to a constraint, the constraint is infeasible. Question 7: A linear programming problem may have more than one set of solutions. Question 8: The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint? Question 9: The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used?

Question 10: In a linear programming problem, the binding constraints for the optimal solution are: 5x1 + 3x2 â‰¤ 30 2x1 + 5x2 â‰¤ 20 Which of these objective functions will lead to the same optimal solution? Question 11: Which of the following statements is not true? Question 12: The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the objective function? Question 13: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. Which of the following points are not feasible? Question 14: Decision variables Question 15: Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet

available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the objective function? Question 16: Which of the following could be a linear programming objective function? Question 17: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. Which of the following constraints has a surplus greater than 0? Question 18: A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your answer in decimal notation. Question 19: Consider the following linear programming problem: Max Z =

$15x + $20y

Subject to:

8x + 5y ≤ 40 0.4x + y ≥ 4 x, y ≥ 0

At the optimal solution, what is the amount of slack associated with the first constraint? Question 20: Consider the following minimization problem: Min z =

x1 + 2x2

s.t.

x1 + x2 ≥ 300

2x1 + x2 ≥ 400 2x1 + 5x2 ≤ 750 x1, x2 ≥ 0

Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25

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MAT 540 Week 8 Assignment Linear Programming Case Study You are a portfolio manager for the XYZ investment fund

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You are a portfolio manager for the XYZ investment fund. The objective for the fund is to maximize your portfolio returns from the investments on four alternatives. The investments include (1) stocks, (2) real estate, (3) bonds, and (4) certificate of deposit (CD). Your total investment portfolio is $1,000,000.

Investment Returns

Based on the returns from the past five years, you concluded that the investment annual returns on stocks are 10%, on real estates are 7% on bonds are 4% and on CD is 1%.

Risk Constraints

However, you also have to analyze the risks associate with each investment category. A wildly used risk measurement parameter is called Value at Risk (VaR). (Note: VaR measures the risk of loss on a specific portfolio of financial assets.) For example, given a million dollar stock investment, if a portfolio of stocks has a one-day 4% VaR, there is a 5% probability that the stock portfolio will fall in value by more than 1,000,000 * 0.004 = $4,000 over a one day period. In the portfolio, the VaR for stock investments is 6%. Similarly, the VaR for real estate investment is 2% and the VaR for bond investment is 1% and the VaR for investment in CD is 0%. To manage the portfolio, you decided that at 5% probability, your VaR for stocks cannot exceed

$25,000, VaR for real estate cannot exceed $15,000, VaR for bonds cannot exceed $2,500 and the VaR for CD investment is $0.

Diversification and Liquidity Constraints

As a diversified investment portfolio, you also decided that each investment category must hold at least $50,000 of the total investment assets. In addition, you must hold combined CD and bond investment no less than $200,000 in order to meet liquidity requirement.

The total amount of real estate holding shall not exceed 30% of the portfolio assets.

A. As a portfolio manager, please formulate and solve the investment portfolio problem using linear programming technique. What are the amounts invest in (1) stocks, (2) real estate, (3) bonds and (4) CD?

B. If $500,000 additional investments are available to you in your portfolio, how would you invest the capital?

C. Would you maintain the portfolio investment if stock yields lowered to 6%? How would you re-distribute your investment portfolio?

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MAT 540 Week 8 Discussion Practice setting up linear programming models for business applications

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www.tutorialrank.com MAT 540 WEEK 8 DISCUSSION

Practice setting up linear programming models for business applications Select an even-numbered LP problem from the text, excluding 14, 20, 22, 36 (which are part of your homework assignment). Formulate a linear programming model for the problem you select.

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MAT 540 Week 8 Homework Chapter 4

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www.tutorialrank.com 1. Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock. Betty stocks three brands of beer- Yodel, Shotz, and Rainwater. The cost per gallon (to the tavern owner) of each brand is as follows:

Brand....................Cost/Gallon Yodel.....................$1.50 Shotz...................... 0.90 Rainwater............... 0.50 The tavern has a budget of $2,000 for beer for Super Bowl Sunday. Betty sells Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon. Based on past football games, Betty has determined the maximum customer demand to be 400 gallons of Yodel, 500 gallons of shotz, and 300 gallons of Rainwater. The tavern has the capacity to stock 1,000 gallons of beer; Betty wants to stock up completely. Betty wants to determine the number of gallons of each brand of beer to order so as to maximize profit. a. Formulate a linear programming model for this problem. b. Solve the model by using the computer.

2. As result of a recently passed bill, a congressman’s district has been allocated $3 million for programs and projects. It is up to the congressman to decide how to distribute the money. The congressman has decide to allocate the money to four ongoing programs because of their importance to his district- a job training program, a parks project, a sanitation project, and a mobile library. However, the congressman wants to distribute the money in a manner that will please the most voters, or, in other words, gain him the most votes in the upcoming election. His staff’s estimates of the number of votes gained per dollar spent for the various programs are as follows. Program....................Votes/Dollar Job training................0.03 Parks.............................0.08 Sanitation....................0.05 Mobile library.............0.03 In order also to satisfy several local influential citizens who financed his election, he is obligated to observe the following guidelines: • None of the programs can receive more than 30% of the total allocation • The amount allocated to parks cannot exceed the total allocated to both the sanitation project and the mobile library. • The amount allocated to job training must at least equal the amount spent on the sanitation project. Any money not spent in the district will be returned to the government; therefore, the congressman wants to spend it all. Thee congressman wants to know the amount to allocate to each program to maximize his votes.

a. Formulate a linear programming model for this problem. b. Solve the model by using the computer.

3. Anna Broderick is the dietician for the State University football team, and she is attempting to determine a nutritious lunch menu for the team. She has set the following nutritional guidelines for each lunch serving: • Between 1,300 and 2,100 calories • At least 4 mg of iron • At least 15 but no more than 55g of fat • At least 30g of protein • At least 60g of carbohydrates • No more than 35 mg of cholesterol She selects the menu from seven basic food items, as follows, with the nutritional contributions per pound and the cost as given: ............ Calories......Iron....Protein ...Carbohydrates....Fat....Cholesterol......Cost ............. (Per lb).......(mg/lb).....(g/lb)........(g/lb)..............(g/lb).........(mg/lb)..........($/lb) Chicken 500 4.2 17 0 30 180 0.85 Fish

480 3.1 85 0 5 90 3.35

Ground beef 840 0.25 82 0 75 350 2.45 Dried beans 590 3.2 10 30 3 0 0.85

Lettuce

40 0.4 6 0 0 0 0.70

Potatoes 450 2.25 10 70 0 0 0.45 Milk (2%) 220 0.2 16 22 10 20 0.82 The dietician wants to select a menu to meet the nutritional guidelines while minimizing the total cost per serving. a. Formulate a linear programming model for this problem and solve. b. If a serving of each of the food items (other than milk) was limited to no more than a half pound, what effect would this have on the solution?

4. Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must determine a schedule for nurses to make sure there are enough of them on duty throughout the day. During the day, the demand for nurses varies. Maureen has broken the day in to twelve 2- hour periods. The slowest time of the day encompasses the three periods from 12:00 A.M. to 6:00 A.M., which beginning at midnight; require a minimum of 30, 20, and 40 nurses, respectively. The demand for nurses steadily increases during the next four daytime periods. Beginning with the 6:00 A.M.- 8:00 A.M. period, a minimum of 50, 60, 80, and 80 nurses are required for these four periods, respectively. After 2:00 P.M. the demand for nurses decreases during the afternoon and evening hours. For the five 2-hour periods beginning at 2:00 P.M. and ending midnight, 70, 70, 60, 50, and 50 nurses are required, respectively. A nurse reports for duty at the beginning of one of the 2-hour periods and works 8 consecutive hours (which is required in the nursesâ€™ contract). Dr. Becker wants to determine a nursing schedule that will meet the hospitalâ€™s minimum requirement throughout the day while using the minimum number of nurses.

a. Formulate a linear programming model for this problem. b. Solve the model by using the computer.

5. The production manager of Videotechnics Company is attempting to determine the upcoming 5-month production schedule for video recorders. Past production records indicate that 2,000 recorders can be produced per month. An additional 600 recorders can be produced monthly on an overtime basis. Unit cost is $10 for recorders produced during regular working hours and $15 for those produced on an overtime basis. Contracted sales per month are as follows: Month Contracted Sales (units) 1 1200 2 2100 3 4 5 2400 3000 4000 Inventory carrying costs are $2 per recorder per month. The manager does not want any inventory carried over past the fifth month. The manager wants to know the monthly production that will minimize total production and inventory costs. a. Formulate a linear programming model for this problem. b. Solve the model by using the computer.

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MAT 540 Week 9 Discussion Application of Integer Programming

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www.tutorialrank.com Week 9 Discussion Explain how the applications of Integer programming differ from those of linear programming. Give specific instances in which you would use an integer programming model rather than an LP model. Provide realworld examples.

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MAT 540 Week 9 Homework Chapter 5

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www.tutorialrank.com MAT 540 Week 9 Homework - Chapter 5 1. Rowntown Cab Company has 70 drivers that it must schedule in three 8-hour shifts. However, the demand for cabs in the metropolitan area varies dramatically according to time of the day. The slowest period is between midnight and 4:00 A.M. the dispatcher receives few calls, and

the calls that are received have the smallest fares of the day. Very few people are going to the airport at that time of the night or taking other long distance trips. It is estimated that a driver will average $80 in fares during that period. The largest fares result from the airport runs in the morning. Thus, the drivers who sart their shift during the period from 4:00 A.M. to 8:00 A.M. average $500 in total fares, and drivers who start at 8:00 A.M. average $420. Drivers who start at noon average $300, and drivers who start at 4:00 P.M. average $270. Drivers who start at the beginning of the 8:00 P.M. to midnight period earn an average of $210 in fares during their 8-hour shift. To retain customers and acquire new ones, Rowntown must maintain a high customer service level. To do so, it has determined the minimum number of drivers it needs working during every 4-hour time segment10 from midnight to 4:00 A.M. 12 from 4:00 to 8:00 A.M. 20 from 8:00 A.M. to noon, 25 from noon to 4:00 P.M., 32 from 4:00 to 8:00 P.M., and 18 from 8:00 P.M. to midnight. a. Formulate and solve an integer programming model to help Rowntown Cab schedule its drivers. b. If Rowntown has a maximum of only 15 drivers who will work the late shift from midnight to 8:00 A.M., reformulate the model to reflect this complication and solve it c. All the drivers like to work the day shift from 8:00 A.M. to 4:00 P.M., so the company has decided to limit the number of drivers who work this 8-hour shift to 20. Reformulate the model in (b) to reflect this restriction and solve it.

2.

2. Juan Hernandez, a Cuban athlete who visits the United States and Europe frequently, is allowed to return with a limited number of consumer items not generally available in Cuba. The items, which are carried in a duffel bag, cannot exceed a weight of 5 pounds. Once Juan is in Cuba, he sells the items at highly inflated prices. The weight and profit (in U.S. dollars) of each item are as follows: Item Weight (lb.) Profit Denim jeans 2 $90 CD players 3 150 Compact discs 1 30 Juan wants to determine the combination of items he should pack in his duffel bag to maximize his profit. This problem is an example of a type of integer programming problem known as a â€œknapsackâ€? problem. Formulate and solve the problem.

3. The Texas Consolidated Electronics Company is contemplating a research and development program encompassing eight research projects. The company is constrained from embarking on all projects by the number of available management scientists (40) and the budget available for R&D projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice versa). Following are the resources requirement and the estimated profit for each project. Project Expense Management Estimated Profit ($1,000s) Scientists required (1,000,000s) 1 50 6 0.30 2 105 8 0.85 3 56 9 0.20 4 45 3 0.15 5 90 7 0.50 6 80 5 0.45 7 78 8 0.55 8 60 5 0.40 Formulate the integer programming model for this problem and solve it using the computer. Corsouth Mortgage Associates is a large home mortgage firm in the southeast. It has a poll of permanent and temporary computer operators who process mortgage accounts, including posting payments and

updating escrow accounts for insurance and taxes. A permanent operator can process 220 accounts per day, and a temporary operator can process 140 accounts per day. On average, the firm must process and update at least 6,300 accounts daily. The company has 32 computer workstations available. Permanent and temporary operators work 8 hours per day. A permanent operator averages about 0.4 error per day, whereas a temporary operator averages 0.9 error per day. The company wants to limit errors to 15 per day. A permanent operator is paid $120 per day wheras a temporary operator is paid $75 per day. Corsouth wants to determine the number of permanent and temporary operators it needs to minimize cost. Formulate, and solve an integer programming model for this problem and compare this solution to the non-integer solution.

5. Globex Investment Capital Corporation owns six companies that have the following estimated returns (in millions of dollars) if sold in one of the next 3 years: Year Sold (estimated returns, $1,000,000s) Company 1 2 3 1 $14 $18 $232 9 11 153 18 23 274 16 21 255 12 16 226 21 23 28 To generate operating funds, the company must sell at least $20 million worth of assets in year 1, $25 million in year 2, and $35 million in year 3. Globex wants to develop a plan for selling these companies during the next 3 years to maximize return. Formulate an integer programming model for this problem and solve it by using the computer.

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MAT 540 Week 9 Quiz 4 Set (Three Sets)

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www.tutorialrank.com MAT 540 Week 9 Quiz 4 Set 1 QUESTIONS Question 1: When using a linear programming model to solve the "diet" problem, the objective is generally to maximize profit. Question 2: In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities. Question 3: In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (â‰¤). Question 4: Fractional relationships between variables are permitted in the standard form of a linear program. Question 5: The standard form for the computer solution of a linear programming problem requires all variables to be to the right and all numerical values to be to the left of the inequality or equality sign

Question 6: A systematic approach to model formulation is to first construct the objective function before determining the decision variables. Question 7: A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the optimal daily profit? Question 8: In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct? Question 9: Balanced transportation problems have the following type of constraints: Question 10: The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint? Question 11: A systematic approach to model formulation is to first

Question 12: The following types of constraints are ones that might be found in linear programming formulations: 1. â‰¤ 2. = 3. > Question 13: The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are $0.40, and for a bag of Vinegar chips $0.50. What is the constraint for salt? Question 14: Small motors for garden equipment is produced at 4 manufacturing facilities and needs to be shipped to 3 plants that produce different garden items (lawn mowers, rototillers, leaf blowers). The company wants to minimize the cost of transporting items between the facilities, taking into account the demand at the 3 different plants, and the supply at each manufacturing site. The table below shows the cost to ship one unit between each manufacturing facility and each plant, as well as the demand at each plant and the supply at each manufacturing facility. What is the demand constraint for plant B? Question 15: Compared to blending and product mix problems, transportation problems are unique because

Question 16: Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock two". The constraint for this requirement can be written as: Question 17: The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.

The constraint for ingredient 3 is: Question 18: Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1. Question 19: Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-

base paint to produce to maximize its total profit. How many gallons of water based paint should the Quickbrush make? Note: Please express your answer as a whole number, rounding the nearest whole number, if appropriate. Question 20: Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel's cat food is made by mixing two types of cat food to obtain the "nutritionally balanced cat diet." The data for the two cat foods are as follows: Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan? Express your answer with two places to the right of the decimal point. For instance, $9.32 (nine dollars and thirty-two cents) would be written as 9.32

MAT 540 Week 9 Quiz 4 Set 2 QUESTIONS Question 1: In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (â‰¤). Question 2: A constraint for a linear programming problem can never have a zero as its right-hand-side value. Question 3: Product mix problems cannot have "greater than or equal to" (â‰Ľ) constraints.

Question 4: In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories. Question 5: In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities. Question 6: When using a linear programming model to solve the "diet" problem, the objective is generally to maximize profit. Question 7: A systematic approach to model formulation is to first Question 8: Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1. Question 9: A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the optimal daily profit? Question 10: The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft

drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint? Question 11: Balanced transportation problems have the following type of constraints: Question 12: In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is Question 13: The following types of constraints are ones that might be found in linear programming formulations: 1. â‰¤ 2. = 3. > Question 14: In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The stockbroker suggests limiting the investments so that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulated as a linear programming constraint? Question 15: The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are

contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.

Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds) 1 20 24 30 2 30 10 50 3 0 30 20 4 24 15 60 5 10 20 40

The constraint for ingredient 3 is:

Question 16: In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct? Question 17: The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of her ingredient) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits

for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the optimal daily profit? Question 18: If Xij = the production of product i in period j, write an expression to indicate that the limit on production of the company's 3 products in period 2 is equal to 400. Question 19: Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel's cat food is made by mixing two types of cat food to obtain the "nutritionally balanced cat diet." The data for the two cat foods are as follows: Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan? Express your answer with two places to the right of the decimal point. For instance, $9.32 (nine dollars and thirty-two cents) would be written as 9.32 Question 20: Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and waterbase paint to produce to maximize its total profit. How many gallons of oil based paint should the Quickbrush make? Note: Please express your answer as a whole number, rounding the nearest whole number, if appropriate.

MAT 540 Week 9 Quiz 4 Set 3 QUESTIONS Question 1: A constraint for a linear programming problem can never have a zero as its right-hand-side value. Question 2: In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities. Question 3: In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the audience exposure. Question 4: The standard form for the computer solution of a linear programming problem requires all variables to be to the right and all numerical values to be to the left of the inequality or equality sign Question 5: When using a linear programming model to solve the "diet" problem, the objective is generally to maximize profit. Question 6: Fractional relationships between variables are permitted in the standard form of a linear program. Question 7: Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock two". The constraint for this requirement can be written as: Question 8: A systematic approach to model formulation is to first Question 9: In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The stockbroker suggests limiting the investments so

that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulated as a linear programming constraint? Question 10: Balanced transportation problems have the following type of constraints: Question 11: Compared to blending and product mix problems, transportation problems are unique because Question 12: A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the optimal daily profit? Question 13: The following types of constraints are ones that might be found in linear programming formulations: 1. â‰¤ 2. = 3. > Question 14: In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct?

Question 15: The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint? Question 16: Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1. Question 17: When systematically formulating a linear program, the first step is Question 18: In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is Question 19: Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-

base paint to produce to maximize its total profit. How many gallons of oil based paint should the Quickbrush make? Note: Please express your answer as a whole number, rounding the nearest whole number, if appropriate. Question 20: Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel's cat food is made by mixing two types of cat food to obtain the "nutritionally balanced cat diet." The data for the two cat foods are as follows: Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan? Express your answer with two places to the right of the decimal point. For instance, $9.32 (nine dollars and thirty-two cents) would be written as 9.32

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MAT 540 Week 10 Discussion Transshipment problems

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Discussion assignment and transshipment problems Select one (1) of the following topics for your primary discussion posting: â€˘ Explain the assignment model and how it facilitates in solving transportation problems. Determine the benefits to be gained from using this model. â€˘ Identify any challenges you have in setting up an transshipment model in Excel, and solving it with Solver. Explain exactly what the challenges are and why they are challenging. Identify resources that can help you with that.

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MAT 540 Week 10 Homework Chapter 6

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www.tutorialrank.com MAT 540 Week 10 Homework Chapter 6 1. Consider the following transportation problem:

From To (Cost) Supply 1 2 3 A 6 5 5 150 B 11 8 9 85 C 4 10 7 125 Demand 70 100 80 Formulate this problem as a linear programming model and solve it by the using the computer.

2. Consider the following transportation problem: From To (Cost) Supply 1 2 3 A 8 14 8 120 B 6 17 7 80 C 9 24 10 150 Demand 110 140 100 Solve it by using the computer.

3. World foods, Inc. imports food products such as meats, cheeses, and pastries to the United States from warehouses at ports in Hamburg, Marseilles and Liverpool. Ships from these ports deliver the products to Norfolk, New York and Savannah, where they are stored in company warehouses before being shipped to distribution centers in Dallas, St. Louis and Chicago. The products are then distributed to specialty foods stores and sold through catalogs. The shipping costs ($/1,000 lb.) from the European ports to the U.S. cities and the available supplies (1000 lb.) at the European ports are provided in the following table: From To (Cost) Supply 4. Norfolk 5. New York 6. Savannah 1. Hamburg 320 280 555 75 2. Marseilles 410 470 365 85 3. Liverpool 550 355 525 40 The transportation costs ($/1000 lb.) from each U.S. city of the three distribution centers and the demands (1000 lb.) at the distribution centers are as follows:

Warehouse Distribution Center 7. Dallas 8. St. Louis 9. Chicago 4. Norfolk 80 78 85 5. New York 100 120 95 6. Savannah 65 75 90 Demand 85 70 65 Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs.

4. The Omega Pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the sales persons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each city is shown in the following table: Salesperson Region (days) A B C D E 1 20 10 12 10 22 2 14 10 18 11 15 3 12 13 19 11 14 4 16 12 14 22 16 5 12 15 19 26 23 Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time.

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MAT 540 Week 10 Quiz 5 (Three Sets)

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www.tutorialrank.com MAT 540 Week 10 Quiz 5 Set 1 QUESTIONS Question 1: Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. Question 2: The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function. Question 3: If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 â‰¤ 1 is a mutually exclusive constraint. Question 4: A conditional constraint specifies the conditions under which variables are integers or real variables. Question 5: If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 + x3 â‰¤ 3 is a mutually exclusive constraint. Question 6: If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3 separate constraints in an integer program. Question 7: The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

Write the constraint that indicates they can purchase no more than 3 machines. Question 8: In a 0-1 integer programming model, if the constraint x1-x2 = 0, it means when project 1 is selected, project 2 __________ be selected. Question 9: Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 ≤ 2) means that __________ out of the 4 projects must be selected. Question 10: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a __________ constraint. Question 11: If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint. Question 12: If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is Question 13: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint. Question 14: If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a __________ constraint. Question 15: Binary variables are Question 16: In a 0-1 integer programming model, if the constraint x1x2 ≤ 0, it means when project 2 is selected, project 1 __________ be selected.

Question 17: The solution to the linear programming relaxation of a minimization problem will always be __________ the value of the integer programming minimization problem. Question 18: In a __________ integer model, some solution values for decision variables are integers and others can be non-integer. Question 19: Max Z = 3x1 + 5x2 Subject to:

7x1 + 12x2 ≤ 136 3x1 + 5x2 ≤ 36 x1, x2 ≥ 0 and integer

Find the optimal solution. What is the value of the objective function at the optimal solution. Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25 Question 20: Consider the following integer linear programming problem Max Z =

3x1 + 2x2

Subject to: 3x1 + 5x2 ≤ 30 5x1 + 2x2 ≤ 28 x1 ≤ 8 x1 ,x2 ≥ 0 and integer Find the optimal solution. What is the value of the objective function at the optimal solution. Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25

MAT 540 Week 10 Quiz 5 Set 2 QUESTIONS Question 1: If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3 separate constraints in an integer program. Question 2: If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 + x3 ≤ 3 is a mutually exclusive constraint. Question 3: Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. Question 4: If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint. Question 5: If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint. Question 6: In a problem involving capital budgeting applications, the 01 variables designate the acceptance or rejection of the different projects. Question 7: The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

Write a constraint to ensure that if machine 4 is used, machine 1 will not be used. Question 8: You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint(s) for the second restriction Question 9: In a 0-1 integer programming model, if the constraint x1-x2 = 0, it means when project 1 is selected, project 2 __________ be selected. Question 10: Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer What is the optimal solution? Question 11: If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a __________ constraint.

Question 12: Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 â‰¤ 2) means that __________ out of the 4 projects must be selected. Question 13: In a 0-1 integer programming model, if the constraint x1x2 â‰¤ 0, it means when project 2 is selected, project 1 __________ be selected. Question 14: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint. Question 15: If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is Question 16: Binary variables are Question 17: The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. Write the constraint that indicates they can purchase no more than 3 machines. Question 18: You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or

S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, the constraint for the first restriction is Question 19: Consider the following integer linear programming problem Max Z =

3x1 + 2x2

Subject to: 3x1 + 5x2 ≤ 30 4x1 + 2x2 ≤ 28 x1 ≤ 8 x1 , x2 ≥ 0 and integer Find the optimal solution. What is the value of the objective function at the optimal solution. Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25 Question 20: Consider the following integer linear programming problem Max Z =

3x1 + 2x2

Subject to: 3x1 + 5x2 ≤ 30 5x1 + 2x2 ≤ 28 x1 ≤ 8 x1 ,x2 ≥ 0 and integer

Find the optimal solution. What is the value of the objective function at the optimal solution. Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25

MAT 540 Week 10 Quiz 5 Set 3 QUESTIONS Question 1: In a problem involving capital budgeting applications, the 01 variables designate the acceptance or rejection of the different projects. Question 2: If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 + x3 ≤ 3 is a mutually exclusive constraint. Question 3: If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3 separate constraints in an integer program. Question 4: In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected, project 1 can not be selected. Question 5: In a mixed integer model, some solution values for decision variables are integer and others are only 0 or 1. Question 6: If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint.

Question 7: You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint(s) for the second restriction Question 8: If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is Question 9: In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation? Question 10: In a 0-1 integer programming model, if the constraint x1x2 â‰¤ 0, it means when project 2 is selected, project 1 __________ be selected. Question 11: In a __________ integer model, some solution values for decision variables are integers and others can be non-integer. Question 12: Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 â‰¤ 2) means that __________ out of the 4 projects must be selected.

Question 13: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint. Question 14: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a __________ constraint. Question 15: You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, the constraint for the first restriction is Question 16: Binary variables are Question 17: Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer What is the optimal solution? Question 18: If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint. Question 19: Max Z = 3x1 + 5x2

Subject to:

7x1 + 12x2 ≤ 136 3x1 + 5x2 ≤ 36 x1, x2 ≥ 0 and integer

Find the optimal solution. What is the value of the objective function at the optimal solution. Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25 Question 20: Consider the following integer linear programming problem Max Z =

3x1 + 2x2

Subject to: 3x1 + 5x2 ≤ 30 4x1 + 2x2 ≤ 28 x1 ≤ 8 x1 , x2 ≥ 0 and integer

Find the optimal solution. What is the value of the objective function at the optimal solution. Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25

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For more course tutorials visit www.tutorialrank.com This Tutorial contains 20 Sets of Final Exam (800 Questions/Answers)

Published on Nov 8, 2019

For more course tutorials visit www.tutorialrank.com This Tutorial contains 20 Sets of Final Exam (800 Questions/Answers)

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