please answer both question .
14. Digital Controls, Inc. (DC) manufactures two models of a radar gun used by police to mon itor 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 re- quires 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. For next week the Newark plant has 600 minutes of injection-molding time available and 1080 min- utes 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: Ceny All Rights Masterpilihan the town which Problems 343 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: Min 10AM + 6BM + 14AP + 9BP S.L. 1AM + + 1AP + = 100 Demand for model A IBM + IBP = 150 Demand for model B 4AM + 3BM $ 600 Injection molding time 6AM + SBM S 1080 Assembly time AM, BM, AP.BP 20 The sensitivity report is shown in Figure 8.19. a. What is the optimal solution and what is the optimal value of the objective function? b. Which constraints are binding? What are the shadow prices? Interpret each. d. If you could change the right-hand side of one constraint by one unit, which one would you choose? Why? C. M Variable Cell Model Variable 5 SC DI D2 Suits Produced Coots Produced Overtime for Cutting Overtime for Sewing Val MOX 150 000 40.000 000 Reded Cat BE O 0 000 -0-000 Olejective Coefficient 190 1500 -15 - 35.000 E. ISCO 10.000 Dec TE+30 23333 172.500 TE10 Shaw Awal Constraints Castrat Number 1 2 1 Cutting time Sewing time Material Overtime Suit minimum Sport Vale ODO 100,000 1.200.000 0.000 100.000 150.000 1500 0.000 34.500 000 - 35.000 0000 Cust RI Side 200.000 INDODO 1.300.000 1000 100.000 25.000 20 JE 133333 JE 10 so whe Dec 500 30.000 300.000 000 100.000 SE30 5 6 mer Problems 345 17. The Porsche Club of America sponsors driver focatie events that provide high performance driving instruction on actual racetracks. Became safety is a primary con sideration at such events, many owners elect toimiall roll bars in their car. Deegan Industries manufactures two types of rollbars Soe Poescher Model DRB is bullied to the car using existing holes in the car's frame. Model DRW is a beavier roll bar that must be welded to the car's frame. Model DRB requires 20 poundsd a special high-alloy steel 40 minutes of manufacturing time, and 60 minutes of ancmbly time. Model DRW requires 25 pounds of the special high-alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Deepam's steel supplier indicated that sent 10.000 pounds of the high-alloy steel will be available ned quarter le addition, Deegan estimates that 2000 hours of manufacturing time and 1600 house my time will be available sex quarter. The profit contributions are $200 per unit for model DRB and 5280 per unit for model DRW. The linear programming model for this problem is as follow Max 2000RR 2800RW BODRS + 2SDRWS 40.000 Selailable ODRB + 100DRW 120.000 Manfacturing minutes CODREAMWS 96.000 Auembly minutes DR. RW 20 The sensitivity report is shown in Figure 8.21. What are the optimal solution and the local peat contributie Another supplier offered to provide Deegan Industries with an additional to pounds of the stoc 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 zwembly 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 prodit is $175 per unit. How would this change in price affect the optimal solution Explain c. If the available manufacturing time is increased by 500 hours, will the shadow price for the manufacturing time constraint change? Explain 14. Digital Controls, Inc. (DCI) manufactures two models of a radar gun used by police to mon- itor 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 re- quires 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. For next week the Newark plant has 600 minutes of injection-molding time available and 1080 min- utes 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: 343 AM BM number of cases of model A manufactured number of cases of model B manufactured number of cases of model A purchased number of cases of model B purchased AP BP The linear programming model that can be used to solve this problem is as follows: Min 10AM + 6BM + 14AP + 9BP S.L. IAM + + TAP + 100 Demand for model A IBM + IBP 150 Demand for model B 4AM + 3BM s 600 Injection molding time 6AM + 8BM s 1080 Assembly time AM. BM, APBPO The sensitivity report is shown in Figure 8.19. What is the optimal solution and what is the optimal value of the objective function? Which constraints are binding? What are the shadow prices? Interpreteach If you could change the right-hand side of one constraint by one unit which one would you choose Why d 17. The Porsche Club of America sponsors driver education events that provide high- performance driving instruction on actual racetracks. Because safety is a primary con- sideration 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 2000 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 DRW. The linear programming model for this problem is as follows: Max 200 DRB + 280DRW s.l. 20DRB + 25 DRW S 40,000 Steel available 40DRB + 100DRW = 120,000 Manufacturing minutes 60DRB + 40DRW . 96.000 Assembly minutes DRB. DRW 20 2 pro $280 per unit for amming model for this problem is as follows: Max 200DRB + 280DRW s.t. 20DRB + 25DRW S 40,000 Steel available 40DRB + 100DRW
