The Racing 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 sports cars. 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 34,000 pounds of the high-alloy steel will be available next quarter. In addition, Deegan estimates that 2,000 hours of manufacturing time and 1,700 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 34,000 40DRB +100DRW 120,000 60DRB + 40DRW 102,000 DRB, DRW Steel available Manufacturing minutes Assembly minutes 0 The computer solution is shown below. Optimal Objective Value - 371200.00000 Value Reduced Cost Variable DRB 400.00000 0.00000 DRW 1040.00000 0.00000 Constraint Slack/Surplus Dual Value 1 0.00000 8.80000 2 0.00000 0.60000 3 0.00000 36400.00000 Objective Allowable Allowable Variable Coefficient DRB DRW 200.00000 280.00000 Constraint RHS Value 1 34000.00000 2 120000.00000 3 102000.00000 Increase Decrease 24.00000 88.00000 220.00000 30.00000 Allowable Increase 8272.72727 15000.00000 Infinite Allowable Decrease 4000.00000 52000.00000 36400.00000 (a) What is the optimal solution and the total profit contribution (in $)? DRB DRW 200 280 total profit contribution $ 372,000 (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? Explain. Yes, the dual value for steel available is 8.8. Each pound of steel will increase profits more than the $2 per pound that the supplier is offering. Yes, there is no surplus of steel so any additional steel that becomes available should be purchased. No, the allowable increase for steel is only 24 pounds, so the additional profits are not applicable for 500 pounds. No, there is a slack value of 8,273, so additional pounds of steel will not increase profits. No, the dual value for steel available is 0.6. Each pound of steel will not increase profits enough to justify the $2 per pound that the supplier is offering. (c) Deegan is considering using overtime to increase the available assembly time. What would you advise Deegan to do regarding this option? Explain. Constraint 1 has a slack. Increasing the number of hours of assembly time will not improve profits. (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. The objective coefficient range for model DRB shows a lower limit of $ 200 . Thus, the optimal solution will not change and the new value will be $ 500 (e) If the available manufacturing time is increased by 500 hours, will the dual value for the manufacturing time constraint change? Explain. The allowable increase is 500 minutes, so the dual value for this constraint will change.