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Subject: Mathematics
Due on: 12/30/2013
Posted On: 12/12/2013 12:02 PM

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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:

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Plant

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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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Tags aignments maths cost plant wine production value dual time total printing determine devoted funds portfolio risk produce battery lakeside reports pfeiffer local news additional fruit juice mexico program order solve litho units

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Tutorial Preview …Optimal xxxxxxxxx Value xxxxxxx 00000 Reduced xxxxxxxx Value Cost xx 20000 xxxxx x 00000 xx 180000 00000 x 00000 SS xxxxx 00000 x xxxxx ST x 00000 0 xxxxx Constraint Slack/Surplus xxxx Value x xxxxx 00000 x 00000 2 x 00000 -0 xxxxx 3 x xxxxx 5 xxxxx 4 0 xxxxx 5 45000 xxxxxxxxx Allowable xxxxxxxxx xxxxxxxxxxx Increase xxxxxxxx 5 25000 xxxxxxxx 0 30000 x 95000 x xxxxx Infinite xxxxxxxxxxxx Analysis BA xxx Homework 3 xxxxxxxxx 5 xxxxx x 55000 xxxxxxxx 5 70000 xxxxxxxx 0 55000 xxx Allowable xxxxxxxxx xxxxx Increase xxxxxxxx 120000 00000 xxxxxxxx 25000 00000 xxxxxx 00000 xxxxx xxxxx 25000 xxxxx 200000 00000 xxxxx 00000 20000 xxxxx 75000 xxxxx xxxxx 00000 xxxxx 00000 Quantitative xxxxxxxx BA 452 xxxxxxxx 3 xxxxxxxxx xx a xxx G = xxxxxx invested in xxxxxx stock xxxx xx amount xxxxxxxx in income xxxxx fund M= xxxxxx invested xx xxxxx market xxxx Max 0 xxx + 0 xxx + x xxx s x 0 10G x 0 05S x 0 xxx x (0 xxxxxxxxxxxx Hartmann's max xxxx G S x (0 xxxxxxxxxxxx xxxxxx fund xxx M ? xx 10)(300,000) Income xxxx min x xx 20)(300,000) xxxxx market min, x + S x M x xxxxxxx Funds xxxxxxxxx G, S, xxx b The xxxxxxxx to xxxxxxxxxx xxxxxxxxx mix xxxxxxx is given xxxxxxx Objective Value xxxxx 00000 xxxxxxxx xxxxx Reduced xxxx G 120000 xxxxx 0 00000 x 30000 xxxxx x 00000 x 150000 00000 x 00000 Constraint xxxxxxxxxxxxx Dual xxxxx x 0 xxxxx 1 55556 x 90000 00000 x 00000 x x 00000 xx 02222 4 xxxxx 00000 0 xxxxx 5 x xxxxx 0 xxxxx Objective Allowable xxxxxxxxx Coefficient Increase xxxxxxxx 0 xxxxx xxxxxxxx 0 xxxxx 0 10000 x 02222 1 xxxxx 0 xxxxx x 14000 x 04000 RHS xxxxxxxxx Allowable Value xxxxxxxx Decrease x xxxxx 8100 xxxxx 8100 00000 x 00000 90000 xxxxx Infinite xxxxxxxxxxxx xxxxxxxx BA xxx Homework 3 xxxxxxxxx 0 00000 xxxxxx 00000 xxxxx xxxxx 0 xxxxx 90000 00000 xxxxxxxx 300000 00000 xxxxxxxx 300000 xxxxx x These xxx given by xxx objective coefficient xxxxxx The xxxxxxxxx xxxxx will xx optimal as xxxx as the xxxxxx remain xx xxx following xxxxxxxxxx Growth stock x 15 ?c1 xx 60 xxxxxx xxxxx No xxxxx Limit < xx ?0 122 xxxxx Market x xx ?c3 xx 20 d xxx dual value xxx the xxxxx xxxxxxxxxx provides xxxx information A xxxxxx in the xxxx index xxxx x 05 xx 0 06 xxxxx increase the xxxxxxxxxx RHS xx xxxx (from xxxxxx to 18,000) xxxx is within xxx right-hand-side xxxxxx xx the xxxx value of…
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Preview: time xxxxxxx to xxxxx and national xxxx is increased xx 1 xxxxxxx xxxxx cost xxxx increase by xxxx Increasing the xxxxxx by xxx xxxxxx will xxxx no effect xxx this constraint xxxxx the xxxx xxxxx is x Quantitative Analysis xx 452 Homework x Questionsa xxx x = xxxxxx of copies xxxx by Benson xxxxxxxx J x xxxxxx of xxxxxx done by xxxxxxx PrintingL = xxxxxx of xxxxxx xxxx by xxxxxxxx LithoMin 2 xxxxx 5J+2 75Ls x BJ?30,000BensonL?50,000Johnson?50,000Lakeside0 xxxx xxxxx 995L=75,000# xxxxxx reportsB-0 1JL?0Benson x Johnson %?30,000Minimum xxxxxxxxxx J,L x xxxxxxxx Solution: x = 4,181, x = 41,806, x = xxxxxxxxxxxxx xxxx Benson xxxxxxxx has a xxxxxxxxx rate of xx instead xx xxx The xxx optimal solution xxxxx increase the xxxxxx assigned xx xxxxxx printing xx 30,000 In xxxx case, the xxxxxxxxxx copies xxxxxxxx xx Benson xxxxxxxx would reduce xx a one-for-one xxxxx the xxxxxx xxxxxxxx to xxxxxxx Printing If xxx Lakeside Litho xxxxxxxxxxx is xxxxxxx xx 1 xxxxx total cost xxxx decrease by xx 2210 xxxxxxxxxxxx xxxxxxxx BA xxx Homework 3 xxxxxxxxxxx a Let xxx number xx xxxxxx battery xxxxx produced at xxx Philippines plantP2= xxxxxx of xxxxxx xxxxxxx packs xxxxxxxx at the xxxxxxxxxxx plantP3= number xx PT-300 xxxxxxx xxxxx produced xx the Philippines xxxxxxxx number of xxxxxx battery xxxxx xxxxxxxx at xxx Mexico plantM2= xxxxxx of PT-200 xxxxxxx packs xxxxxxxx xx the xxxxxx plantM3= number xx PT-300 battery xxxxx produced xx xxx Mexico.....
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