Question;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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