MAT 540 Entire Course

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MAT 540 Week 1 DQ 1 Gallup Poll MAT 540 Week 1 DQ 2 Qualitative vs. Quantitative MAT 540 Week 2 DQ 1 Scatter Plot MAT 540 Week 2 DQ 2 Correlation and Causation MAT 540 Week 3 DQ 1 Actuaries MAT 540 Week 3 DQ 2 Probability Video Analysis MAT 540 Week 4 DQ 1 Normal or Bell-Shaped Curve MAT 540 Week 4 DQ 2 Standardized Testing MAT 540 Week 5 DQ 1 Repeated Sampling MAT 540 Week 5 DQ 2 Confidence Intervals MAT 540 Week 6 DQ 1 Statistical Concept MAT 540 Week 6 Final Paper

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MAT 540 Final Exam (20 Sets)

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This Tutorial contains 20 Sets of Final Exam (800 Questions/Answers)

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MAT 540 Midterm Exam (5 Sets)

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This Tutorial contains 5 Sets of Midterm Exam

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 350

.10

400

.18

450

.50

Probability

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 1

7

10

2

12

15

3

18

20

4

22

Forecast

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

p(xi)

.10

1 .15

2 .18

3 .20

4

5 .20

6 .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 1

7

10

2

12

15

3

18

20

4

22

Forecast

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 l ==============================================

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

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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. ==============================================

MAT 540 Week 1 Quiz 1 (Ash)

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MAT 540 Week 1 Quiz 1 ==============================================

MAT 540 Week 1-10 All Homework

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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 2 Assignment 1 Final Paper Draft

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MAT 540 Week 2 Assignment 1 Final Paper Draft ==============================================

MAT 540 Week 2 Homework Chapter 12

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MAT540

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: ==============================================

MAT 540 Week 2 Quiz 2

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MAT 540 Week 2 Quiz 2 ==============================================

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. ==============================================

MAT 540 Week 3 Quiz 3 (Ash)

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mat 540 week 3 quiz 3 ==============================================

MAT 540 Week 4 Homework Chapter 15

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MAT 540 Homework Chapter 15

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. 0.4

Compute an exponential smoothed forecast, using an Îą value of

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.)

9

17

14

25

10

8

12

7

15

14

Permits

9

7

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 4 Quiz 4 (Ash)

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MAT 540 Week 4 Quiz 4 ==============================================

MAT 540 Week 6 Final Paper

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Focus of the Final Paper In this six- to eight-page research paper, you will explore in detail one of the statistical approaches to research discussed in the course, applying it in the context of a specific application or methodological study. This will help you gain a deeper understanding of your chosen topic, as well as gain experience in translating these ideas into practice. Select a topic for your research paper using any of the statistical methods that we discussed in the course as it relates to your area of

interest in either business, economics, finance, management, social science, health, psychology or education. Find at least three (3) relevant research articles which: support your chosen topic. discuss previous work on modeling/analysis in the area youâ€™ve selected. have the statistical analysis and results from research conducted. cover technical aspects of the statistical methods discussed in class. These can be found in the Ashford Online Library by going to a research database such as JSTOR or ProQuest and searching for your topic. If available, narrow your search category to scholarly journals, including peer-reviewed and full-text documents only. At least three of your sources must be from peer-reviewed scholarly journals. Introduction Describe, in third person, the issue youâ€™ve selected, why it was selected, the perspective of the approach, and the scope of the paper. The introduction describes what will be covered in the paper, and serves to engage the reader. Be specific and to the point. Statement of the Problem Describe, in third person, why the topic is relevant, and a problem or issue associated with the topic. It is important to provide scholarly sources in support of your discussion of the problem or issue. Literature Review In the literature review, process and develop a conceptual framework of the issue or problem that is being researched. This section should

present a comprehensive review of the historical and current literature on the topic. The literature review should: Identify the topic, and describe specific research related to the topic (describe the study, sample, findings, important points from the discussion in the research â€“ describe any variables that may influence the findings of the research). Address any key issues such as political, social, legal, and/or ethical implications the literature reports. If there are pros and cons of a topic/issue, explore holistically a review of the literature reflecting alternative positions. This section should demonstrate understanding of the literature in support of a hypothesis or research question. It should not be formatted as a series of article abstracts. Conclusion In the conclusion, summarize what the paper covered. Restate the research questions or hypothesis. Discuss: why the topic was selected; the problem/issue briefly stated; the approach that was used; findings; solutions and suggestions or ideas that you as the researcher may have. A reader should be able to preview the conclusion and understand the purpose of the paper, and the results of the research. References Provide a reference page listing all sources used in the development of this paper in American Psychology Association (APA) format. All literature/computer/interview/resources should be cited and listed. ==============================================

MAT 540 Week 6 Homework Chapter 2

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MAT 540 Week 6 Homework Chapter 2

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 Related Tutorials ==============================================

MAT 540 Week 7 Homework Chapter 3

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MAT 540 Week 7 Homework Chapter 3

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? ==============================================

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

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Week 8 Project

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? ==============================================

MAT 540 Week 8 Homework Chapter 4

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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 congressmanâ€™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 staffâ€™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

â€˘ At least 60g of carbohydrates â€˘ 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 2hour 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. ==============================================

MAT 540 Week 9 Homework Chapter 5

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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. ==============================================

MAT 540 Week 10 Homework Chapter 6

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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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