# maths assignments

Question # 00005219 Posted By: spqr Updated on: 12/12/2013 12:02 PM Due on: 12/30/2013
Subject Mathematics Topic General Mathematics Tutorials:
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Quantitative Analysis BA 452 Homework 3 Questions

27. Golf Shafts, Inc. (GSI), produces graphite shafts for several manufacturers of golf clubs. Two GSI manufacturing facilities, one located in San Diego and the other in Tampa, have the capability to produce shafts in varying degrees of stiffness, ranging from regular models used primarily by average golfers to extra stiff models used primarily by low-handicap and professional golfers. GSI just received a contract for the production of 200,000 regular shafts for previous orders, neither plant has sufficient capacity by itself to fill the new order. The San Diego plant can produce up to a total of 180,000 shafts. Because the equipment differences at each of the plants and differing labor costs, the per-unit production costs vary as shown here:

 San Diego Cost Tampa Cost Regular shaft \$5.25 \$4.95 Stiff shaft \$5.45 \$5.70

a. Formulate a linear programming model to determine how GSI should schedule production for the new order in order to minimize the total production cost.

b. Solve the model that you developed in part (a).

c. Suppose that some of the previous orders at the Tampa plant could be rescheduled in order to free up additional capacity for the new order. Would this option be worthwhile? Explain.

d. Suppose that the cost to produce a stiff shaft in Tampa had been incorrectly computed, and that the correct cost is \$5.30 per shaft. What effect, if any, would the correct cost have on the optimal solution developed in part (b)? What effect would it have on the total production cost?

Quantitative Analysis BA 452 Homework 3 Questions

28. The Pfeiffer Company manages approximately \$15 million for clients. For each client, Pfeiffer choose a mix of three investment vehicles: a growth stock fund, an income fund, and a money market fund. Each client has different investment objectives and different tolerances for risk. To accommodate these differences, Pfeiffer places limits on the percentage of each portfolio that may be invested in the three funds and assigns a portfolio risk to each client.

Here’s how the system works for Dennis Hartman, one of Pfeiffer’s clients. Based on an evaluation of Hartmann’s risk tolerance, Pfeiffer has assigned Hartmann’s portfolio a risk index of 0.05. Furthermore, to maintain diversity, the fraction of Hartmann’s portfolio invested in the growth and income funds must be at least 10% for each, and at least 20% must be in the money market fund.

The risk ratings for the growth, income, and money market funds are 0.10, 0.05, and 0.01, respectively. A portfolio risk index is computed as a weighted average of the risk ratings for the three funds where the weights are the fraction of the portfolio invested in each of the funds. Hartmann has given Pfeiffer \$300,000 to manage. Pfeiffer is currently forecasting a yield of 20% growth fund, 10% on the income fund, and 6% on the money market fund.

a. Develop a linear programming model to select the best mix of investments for Hartmann’s portfolio.

b. Solve the model you developed in part (a).

c. How much may the yields on the three funds vary before it will be necessary for Pfeiffer to modify Hartmann’s portfolio?

d. If Hartmann were more risk tolerant, how much of a yield increase could be expect? For instance, what if his portfolio risk index is increased to 0.06?

e. If Pfeiffer revised the yield estimate for the growth fund downward to 0.10, how would you recommend modifying Hartmann’s portfolio?

f. What information must Pfeiffer maintain on each client in order to use this system to manage client portfolios?

g. On a weekly basis Pfeiffer revises the yield estimates for the three funds. Suppose Pfeiffer has 50 clients. Describe how you would envision Pfeiffer making weekly modifications in each client’s portfolio and allocating the total funds managed among the three investment funds.

Quantitative Analysis BA 452 Homework 3 Questions

29. La Jolla Beverage Products is considering producing a wine cooler that would be a blend of white wine, a rose wine, and fruit juice. To meet taste specifications, the wine cooler must consist of at least 50% white wine, at least 20% and no more than 30% rose wine, and exactly 20% fruit juice. La Jolla purchases wine from local wineries and the fruit juice from a processing plant in San Francisco. For the current production period, 10,000 gallons of white wine and 8,000 gallons of rose wine can be purchased; an unlimited amount of fruit juice can be ordered. The costs for the wine are \$1.00 per gallon for the white and \$1.50 per gallon for the rose; the fruit juice can be purchased for \$0.50 per gallon. La Jolla Beverage Products can sell all of the wine cooler they produce for \$2.50 per gallon.

a. Is the cost of the wine and fruit juice a sunk cost or a relevant cost in this situation? Explain.

b. Formulate a linear program to determine the blend of the three ingredients that will maximize the total profit contribution. Solve the linear program to determine the number of gallons of each ingredient La Jolla should purchase and the total profit contribution they will realize from this blend.

c. If La Jolla could obtain additional amounts of the white wine, should they do so? If so, how much should they be willing to pay for each additional gallon, and how many additional gallons would they want to purchase?

d. If La Jolla Beverage Products could obtain additional amounts of the rose wine, should they do so? If so, how much should they be willing to pay for each additional gallon, and how many additional gallons would they want to purchase?

e. Interpret the dual value for the constraint corresponding to the requirement that the wine cooler must contain at least 50% white wine. What is your advice to management given this dual value?

f. Interpret the dual value for the constraint corresponding to the requirement that the wine cooler must contain exactly 20% fruit juice. What is your advice to management given this dual value?

Quantitative Analysis BA 452 Homework 3 Questions

30. The program manager for Channel 10 would like to determine the best way to allocate the time for the 11:00-11:30 evening news broadcast. Specifically, she would like to determine the number of minutes of broadcast time to devote to local news, national news, weather, and sports. Over the 30-minute broadcast, 10 minutes are set aside for advertising. The station’s broadcast policy states that at least 15% of the time available should be devoted to local news coverage; the time devoted to local news or national news must be at least 50% of the total broadcast time; the time devoted to the weather segment must be less than or equal to the time devoted to the sports segment; the time devoted to the sports segment should be no longer than the total time spent on the local and national news; and at least 20% of the time should be devoted to the weather segment. The production costs per minute are \$300 for local news, \$200 for national news, \$100 for weather, and \$100 for sports.

a. Formulate and solve a linear program that can determine how the 20 available minutes should be used to minimize the total cost of producing the program.

b. Interpret the dual value for the constraint corresponding to the available time. What advice would you give the station manager given this dual value?

c. Interpret the dual value for the constraint corresponding to the requirement that at least 15% of the available time should be devoted to local coverage. What advice would you give the station manager given this dual value?

d. Interpret the dual value for the constraint corresponding to the requirement that the time devoted to the local and the national news must be at least 50% of the total broadcast time. What advice would you give the station manager given this dual value?

e. Interpret the dual value for the constraint corresponding to the requirement that the time devoted to the weather segment must be less than or equal to the time devoted to the sports segment. What advice would you give the station manager given this dual value?

Quantitative Analysis BA 452 Homework 3 Questions

31. Gulf Coast Electronics is ready to award contracts for printing their annual report. For the past several years, the four-color annual report has been printed by Johnson Printing and Lakeside Litho. A new firm, Benson Printing, inquired into the possibility of doing a portion of the printing. The quality and service level provided by Lakeside Litho has been extremely high; in fact, only 0.5% of their reports have had to be discarded because of quality problems. Johnson Printing has also had a high quality level historically, producing an average of only 1% unacceptable reports. Because Gulf Coast Electronics has had no experience with Benson Printing, they estimated their defective rate to be 10%. Gulf Coast would like to determine how many reports should be printed by each firm to obtain 75,000 acceptable-quality reports. To ensure that Benson Printing will receive some of the contract, management specified that the number of reports awarded to Benson Printing must be at least 10% of the volume given to Johnson Printing. In addition, the total volume assigned to Benson Printing, Johnson Printing, and Lakeside Litho should not exceed 30,000, 50,000, and 50,000 copies, respectively. Because of the long-term relationship with lakeside Litho, management also specified that at least 30,000 reports should be awarded to Lakeside Litho. The cost per copy is \$2.45 for Benson Printing, \$2.50 for Johnson Printing, and \$2.75 for Lakeside Litho.

a. Formulate and solve a linear program for determining how many copies should be assigned to each printing firm to minimize the total cost of obtaining 75,000 acceptable quality reports.

b. Suppose that the quality level for Benson Printing is much better than estimated. What effect, if any, would this quality level have?

c. Suppose that management is willing to reconsider their requirement that the Lakeside Litho be awarded at least 30,000 reports. What effect, if any, would this consideration have?

Quantitative Analysis BA 452 Homework 3 Questions

32. PhotoTech, Inc., a manufacturer of rechargeable batteries for digital cameras, signed a contract with a digital photography company to produce three different lithium-ion battery packs for a new line of digital cameras. The contract calls for the following:

 Battery Pack Production Quantity PT-100 200,000 PT-200 100,000 PT-300 150,000

PhotoTech can manufacture the battery packs at manufacturing plants located in the Philippines and Mexico. The unit cost of the battery packs differs at the two plants because of differences in production equipment and wage rates. The unit costs for each battery pack at each manufacturing plant are as follows:

Plant

 Product Philippines Mexico PT-100 \$0.95 \$0.98 PT-200 \$0.98 \$1.06 PT-300 \$1.34 \$1.15

The PT-100 and PT-200 battery packs are produced using similar production equipment available at both plants. However, each plant has a limited capacity for the total number of PT-100 and PT-200 battery packs produced. The combined PT-100 and PT-200 production capacities are 175,000 units at the Philippines plant and 160,000 units at the Mexico plant. The PT-300 production capacities are 75,000 units at the Philippines plant and 100,000 units at the Mexico plant. The cost of shipping from the Philippines plant is \$0.18 per unit, and the cost of shipping from the Mexico plant is \$0.10 per unit, and the cost of shipping from the Mexico plant is \$0.10 per unit.

a. Develop a linear program that PhotoTech can use to determine how many units of each battery pack to produce at each plant in order to minimize the total production and shipping cost associated with the new contract.

b. Solve the linear program developed in part (a) to determine the optimal production plan.

c. Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change in order to produce additional units of the PT-100 in the Philippines plant.

d. Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change in order to produce additional units of the PT-200 in the Mexico plant.

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1. ## Solution: maths assignments

Tutorial # 00005012 Posted By: spqr Posted on: 12/12/2013 12:11 PM
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Optimal Objective Value 1404750.00000 Reduced Variable Value Cost RS 20000.00000 0.00000 ST 180000.00000 0.00000 SS 75000.00000 0.00000 ...
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