MAT 540 Final Exam (20 Sets)

For more classes visit www.snaptutorial.com This Tutorial contains 20 Sets of Final Exam (800 Questions/Answers) *********************************************************************

MAT 540 Midterm Exam (5 Sets)

For more classes visit www.snaptutorial.com 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 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 frame:

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MAT 540 Week 1 Discussion Class Introductions

For more classes visit www.snaptutorial.com "Class Introductions" Please respond to the following: â&#x20AC;˘ 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 *********************************************************************

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

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www.snaptutorial.com MAT 540 Week 1 Homework Chapter 1 1. The Retread Tire Company 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 1-10 All Homework

For more classes visit www.snaptutorial.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 *********************************************************************

MAT 540 Week 1-11 All Discussion Question

For more classes visit www.snaptutorial.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 *********************************************************************

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

For more classes visit www.snaptutorial.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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In your own words, explain how to obtain the â&#x20AC;&#x153;expected value of perfect informationâ&#x20AC;? 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

For more classes visit www.snaptutorial.com 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 1 (3 Sets)

For more classes visit www.snaptutorial.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 that 20 people will attend, what price should be charged per person to 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 breakeven 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. *********************************************************************

MAT 540 Week 3 Discussion Simulation

For more classes visit www.snaptutorial.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&#x20AC;&#x153;runningâ&#x20AC;? , 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)

For more classes visit www.snaptutorial.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 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 Warm Rainy S1 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. *********************************************************************

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: • 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. • 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. *********************************************************************

MAT 540 Week 4 Homework Chapter 15

For more classes visit www.snaptutorial.com 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 City’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. Determine the strength of the causal relationship between monthly sales and new home construction by using correlation. 5. The manager of Gilleyâ&#x20AC;&#x2122;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

For more classes visit www.snaptutorial.com "Reflection to dateÂ? Please respond to the following: In a paragraph, reflect on what you've learned so far in this course. Identify the most

interesting, unexpected, or useful thing you've learned and explain why

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MAT 540 Week 6 Discussion LP Models

For more classes visit www.snaptutorial.com Discuss LP Models Select one (1) of the following topics for your primary discussion posting: â&#x20AC;˘ 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&#x20AC;˘ 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

For more classes visit www.snaptutorial.com 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 resources- labor 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 board-ft. 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 *********************************************************************

MAT 540 Week 7 Discussion sensitivity analysis

For more classes visit www.snaptutorial.com Discuss sensitivity analysis Select one (1) of the following topics for your primary discussion posting: â&#x20AC;˘ 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&#x20AC;˘ Explain what the shadow price means in a maximization problem. Explain what this tells us from a management perspective. *********************************************************************

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 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 Bradleys’ 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 7 Quiz 3 (Three Sets)

For more classes visit www.snaptutorial.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 ≥ 20 Question 3: In minimization LP problems the feasible region is always below the 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 *********************************************************************

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

For more classes visit www.snaptutorial.com 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?

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

For more classes visit www.snaptutorial.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

For more classes visit www.snaptutorial.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 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&#x20AC;&#x2122; contract). Dr. Becker wants to determine a nursing schedule that will meet the hospitalâ&#x20AC;&#x2122;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

For more classes visit www.snaptutorial.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 real-world examples.

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MAT 540 Week 9 Homework Chapter 5

For more classes visit www.snaptutorial.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 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)

For more classes visit www.snaptutorial.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&#x2030;¤). 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 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

For more classes visit www.snaptutorial.com Discussion assignment and transshipment problems Select one (1) of the following topics for your primary discussion posting: â&#x20AC;˘ Explain the assignment model and how it facilitates in solving transportation problems. Determine the benefits to be gained from using this model. â&#x20AC;˘ 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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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)

For more classes visit www.snaptutorial.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&#x2030;¤ 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&#x2030;¤ 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 x1x2 = 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 â&#x2030;¤ 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 â&#x2030;¤ 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,

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# MAT 540(Str) Education Specialist -snaptutorial.com

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

# MAT 540(Str) Education Specialist -snaptutorial.com

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