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Question;14.;Digital Controls, Inc. (DCI), manufactures two;models of a radar gun used by police to monitor the speed of automobiles. Model;A has an accuracy of plus or minus 1 mile per hour, whereas the smaller model B;has an accuracy of plus or minus 3 miles per hour. For the next week, the;company has orders for 100 units of model A and 150 units of model B. Although;DCI purchases all the electronic components used in both models, the plastic;cases for both models are manufactured at a DCI plant in Newark, New Jersey.;Each model A case requires 4 minutes of injection-molding time and 6 minutes of;assembly time. Each model B case requires 3 minutes of injection-molding time;and 8 minutes of assembly time. Each model B case requires 3 minutes of;injection-molding time and 8 minutes of assembly time. For next week, the;Newark plant has 600 minutes of injection-molding time available and 1080;minutes of assembly time available. The manufacturing cost is $10 per case for;model A and $6 per case for model B. Depending upon demand and the time;available at the Newark plant, DCI occasionally purchases cases for one or both;models from an outside supplier in order to fill customer orders that could not;be filled otherwise. The purchase cost is $14 for each model A case and $9 for;each model B case. Management wants to develop a minimum cost plan that will;determine how many cases of each model should be produced at the Newark plant;and how many cases of each model should be purchased. The following decision;variables were used to formulate a linear programming model for this problem;AM=number of cases of model A manufactured;BM=number of cases of model B manufactured;AP=number of cases of model A purchased;BP=number of cases of model B purchased;The linear programming model that can be used;to solve this problem is as follows;10;+ 6 + 14 + 9..;1;+;+;1 +;= 100;1;+;1 = 150;4;+ 3;? 600;6;+ 8;? 1080;? 0;Quantitative;Analysis BA 452 Homework 3 Questions;The computer solution is shown in Figure 3.18.;a. What is the optimal solution and what is the;optimal value of the objective function?;b. Which constraints are binding?;c. What are the dual values? Interpret each.;d. If you could change the right-hand side of one;constraint by one unit, which one would you choose? Why?;Quantitative;Analysis BA 452 Homework 3 Questions;15.;Refer to;the computer solution to Problem 14 in Figure 3.18.;a. Interpret the ranges of optimality for the;objective function coefficients.;b.;Suppose;that the manufacturing cost increases to $11.20 per case for model A. What is;the new optimal solution?;c.;Suppose;that the manufacturing cost increases to $11.20 per case for model A and the;manufacturing cost for model B decreases to $5 per unit. Would the optimal;solution change?;Quantitative;Analysis BA 452 Homework 3 Questions;16.;Tucker Inc.;produces high-quality suits and sport coats for men. Each suit requires 1.2;hours of cutting time and 0.7 hours of sewing time, uses 6 yards of material;and provides a profit contribution of $190. Each sport coat requires 0.8 hours;of cutting time and 0.6 hours of sewing time, uses 4 yards of material, and;provides a profit contribution of $150. For the coming week, 200 hours of;cutting time, 18- hours of sewing time, and 1200 yards of fabric are available.;Additional cutting and sewing time can be obtained by scheduling overtime for;these operations. Each hour of overtime for the cutting operation increase the;hourly cost by $15, and each hour of overtime for the sewing operation increase;the hourly cost by $10. A maximum of 100 hours of overtime can be scheduled.;Marketing requirements specify a minimum production of 100 suits and 75 sport;coats. Let;S=number of suits produced;SC=number of sport oats produced;D1=hours of overtime for the cutting operation;D2=hours of overtime for the sewing operation;The computer solution is shown in Figure 3.19.;a.;What is the;optimal solution, and what is the total profit? What is the plan for the use of;overtime?;b.;A price increase fir suits is being considered;that would result in a profit contribution of $210 per suit. If this price;increase is undertaken, how will the optimal solution change?;c.;Discuss the;need for additional material during the coming week. If a rush order for;material can be placed at the usual price plus an extra $8 per yard for;handling, would you recommend the company consider placing a rush order for;material? What is the maximum price Tucker would be willing to pay for an;additional yard of material? How many additional yards of material should;Tucker consider ordering?;d.;Suppose the;minimum production requirement for suits is lowered to 75. Would this change;help or hurt profit? Explain.;Quantitative;Analysis BA 452 Homework 3 Questions;Quantitative;Analysis BA 452 Homework 3 Questions;17.;The Porsche Club of America sponsors driver;education events that provide high-performance;driving instruction on actual race tracks.;Because safety is a primary consideration at such events;many owners elect to install roll bars in their;cars. Deegan Industries manufactures two types of roll;bars for Porsches. Model DRB;is bolted to the car using existing holes in the car?s frame. Model DRW;is a heavier roll bar that must be welded to;the car?s frame. Model DRB requires 20 pounds of a;special high alloy steel, 40 minutes of;manufacturing time, and 60 minutes of assembly time. Model;DRW requires 25 pounds of the special high;alloy steel, 100 minutes of manufacturing time, and 40;minutes of assembly time.;Deegan?s steel supplier indicated that at most 40,000 pounds of the high-;alloy steel will be available next quarter. In;addition, Deegan estimates that 20000 hours of;manufacturing time and 1600 hours of assembly;time will be available next quarter. The profit;contributions are $200 per unit for model DRB;and $280 per unit for model DRB. The linear;programming model for this problem is as;follows;200+..;20+ 25? 40,000;40+ 100? 120,000;60+ 40? 96,000,? 0;The computer solution is shown in Figure 3.20.;a. What are the optimal solution and the total;profit contribution/;b.;Another;supplier offered to provide Deegan Industries with an additional 500 pounds of;the steel alloy at $2 per pound. Should Deegan purchase the additional pounds;of the steel alloy? Explain.;c. Deegan is considering using overtime to increase;the available assembly time. What would you advise Deegan to do regarding this;option? Explain.;d.;Because of;increased competition, Deegan is considering reducing the price of model DRB;such that the new contribution to profit is $175 per unit. How would this;change in price affect the optimal solution? Explain.;e. If the available manufacturing time is increased;by 500 hours, will the dual value for the manufacturing time constraint change?;Explain.;Quantitative;Analysis BA 452 Homework 3 Questions;Quantitative;Analysis BA 452 Homework 3 Questions;18.;Davison;Electronics manufactures two LCD television monitors, identified as model A and;model B. Each model has its lowest possible production cost when produced on;Davison?s new production line. However, the new production line does not have;the capacity to handle the total production of both models. As a result, as;least some of the production must be routed to a higher-cost, old production;line. The following table shows the minimum production requirements for next;month, the production line table shows the minimum production requirements for;next month, the production line capacities in units per month, and the;production cost per unit for each production line;Production Cost per;Unit;Model;New Line;Old Line;Minimum;Production;Requirements;A;$30;$50;50,000;B;$25;$40;70,000;Production Line;80,000;60,000;Capacity;Let;AN= Units of model A produced on the new production line;AO= Units of model A produced on the old production line;BN = Units of model B produced on the new production line;BO= Units of model B produced on the old production line;Davison?s objective is to determine the minimum;cost production plan. The computer solution is shown below.;a. Formulate the linear programming model for this;problem using the following four constraints;i. Constraint 1: Minimum production for model A;ii. Constraint 2: Minimum production for model B;iii. Constraint 3: Capacity of the new production line;iv. Constraint 4: Capacity of the old production line;b.;Using;computer solution in Figure 3.21, what is the optimal solution, and what is the;total production cost associated with this solution?;c. Which constraints are binding? Explain.;d.;The;production manager noted that the only constraint with a positive dual values;is the constraint on the capacity of the new production line. The manager?s;interpretation of the dual value was that a one-unit increase in the right-hand;side of this constraint would actually increase the total production cost by;$15 per unit. Do you agree with this interpretation? Would an increase in;capacity for the new production line be desirable? Explain.;e. Would you recommend increasing the capacity of;the old production line? Explain.;Quantitative;Analysis BA 452 Homework 3 Questions;f.;The;production cost for model A on the old production line is $50 per unit. How;much would this cost have to change to make it worthwhile to produce model A on;the old production line? Explain.;g.;Suppose;that the minimum production requirement for model B is reduced from 70,000;units to 60,000 units. What effect would this change have on the total;production cost? Explain.;Optimal Objective Value;= 3850000.00000;Variable;Value;Reduced Cost;AN;50000.00000;0.00000;AO;0.0000;5.00000;BN;30000.00000;0.00000;BO;40000.00000;0.00000;Constraint;Slack/Surplus;Dual Value;1;0.00000;45.00000;2;0.00000;40.00000;3;0.00000;-15.00000;4;20000.00000;0.00000;OBJECTIVE COEFFICIENT RANGES;Variable;Objective Coefficient;Allowable Increase;Allowable Decrease;AN;30.00000;5.00000;Infinite;AO;50.00000;Infinite;5.00000;BN;25.00000;15.00000;5.00000;BO;40.00000;5.00000;15.00000;RIGHT HAND SIDE RANGES;Constraint;RHS Value;Allowable Increase;Allowable Decrease;1;50000.00000;20000.00000;40000.00000;2;70000.00000;20000.00000;40000.00000;3;80000.00000;40000.00000;20000.00000;4;60000.00000;Infinite;20000.00000

Paper#61163 | Written in 18-Jul-2015

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