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 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.t. 20DRB + 25DRW S 40000 Steel available 40DRB + 100DRW < 120000 Manufacturing minutes 60DRB + 40DRW S 96000 Assembly minutes DRB, DRW 20 SUDRB + 40DRW S 96000 Assembly minutes DRB, DRW 0 e sensitivity report is shown in the figure below. Optimal Objective Value = Variable DRB DRW 424000.00000 Value Reduced Cost 1000.00000 0.00000 800.00000 0.00000 Constraint Slack/Surplus Dual Value 1 5.00000 8.80000 23 0.00000 0.60000 4000.00000 0.00000 Objective Allowable Allowable Variable Coefficient Increase Decrease DRB 200.00000 24.00000 88.00000 DRW 280.00000 220.00000 30.00000 RHS Allowable Allowable Constraint Value Increase Decrease 1 40000.00000 909.09091 10000.00000 2 120000.00000 40000.00000 5714.28571 3 96000.00000 Infinite 4000.00000 a. What are the optimal solution and the total profit contribution? DRB 1,000 units DRW 800 units Total profit contribution = $ 424,000 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? Round your answers to two decimals. Yes because it has a shadow price of $ 8.8 and this price is valid for an additional 909.09 pounds of steel. c. Deegan is planning to consider using overtime to increase the available assembly time. Should Deegan consider using overtime? hours. Increasing the number of hours of assembly time Constraint 3 (assembly time) has a of worthwhile. DOR cuch that the new contribution to profit is 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? The optimal solution | $175 is Profit=$ change as long as the objective coefficient for model DRB is between $ this range so the optimal solution, and e. If the available manufacturing time is increased by 500 hours, will the dual value for the manufacturing time constraint change? If required, round your answer for dual value to two decimal places. If the manufacturing time is increased by 500 hours, which is minutes, the dual value of $ per minute: change because the allowable increase is 35,714.2 minutes