Question 1 (40 points) Listen The Poniche Club of America sponsors driver education events that provide high performance driving instruction on cancer, Because safety is a primary cold trations when we let staro bars in their curs Decladustries maste types of roll is for Porsche Model DRD is bold to the curing tog boles in the car's Model DRW is havior old her that the welded to the car' frame. Model DR requires 20 push of a special high alloy wel 10 min ving time and minutes of Model DRW roques 25 pounds of the special high alloy stol 100 minutes of manufacturing time, and 40 minutes of toe. Dee's supplier in 10.000 pounds of the Nigh alloy steel will be waloble el que In Dreams 2000 bon of manfacturing time and 1600 house will be able The DRW pero con 200 port for model 20 The programming model for the problem is to Max 2000-200RW SE DRW 000S RODRW 1200 M GOD OOR.000 DARO The solution is shows in Figure 1.30 FIGURE 110 TON NORTHEASINGTON VAL What are the optimal solution? (Write your answer as integers. For example, 500). The optimal DRB- and DRW- The optimal profit is (Don't write the $ sign or comma in your answer! Write your answer as integers. For example, 5000) The Porsche Club of America sponsors driver education events that provide high- performance driving instruction on actual race tracks. Because safety is a primary consid- eration 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 200DRB + 280DRW S.L. 20DRB + 25DRWS 40,000 Steel available 40DRB + 100DRW = 120,000 Manufacturing minutes 60DRB + 40DRW S 96.000 Assembly minutes DRB. DRW 20 The computer solution is shown in Figure 3.20. FIGURE 3.20 THE SOLUTION FOR THE DEEGAN INDUSTRIES PROBLEM Optimal objective Valuan 420000.000 Variable Vete Reduced coat DRA DRW 100000000 300.00000 ID000 000000 constraint Black/Burplus buat va 0.00000 0.00000 400000000 8.80000 0.600DD 0.0000 Variable Obiective conficient Allowable Therese Allowable Decrease DRE DAN 2001 00000 20-00000 24.00000 220.00000 B000000 3000000 Contraint Value Allowable ins Allowable Degree 40000.000 12000000000 000.00000 90909091 1000000000 1000000000 5114262 3000.00000
