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, manyowners 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 isa 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 DRWrequires 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-alloysteel will be available next quarter. In addition, Deegan estimates that 2,000 hours of manufacturing time and 1,800 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:Maxs.t.200DRB + 280DRW20DRB + 25DRW40DRB + 100DRW60DRB + 40DRWThe computer solution is shown below.Optimal Objective Value = 371200.00000VariableDRBDRWConstraint123Variable<34,000 Steel available≤ 120,000 Manufacturing minutes≤ 108,000 Assembly minutesDRB, DRW >0DRBDRWConstraint123Value400.000001040.00000Reduced Cost0.000000.00000Slack/Surplus0.000000.0000042400.00000200.00000280.00000Objective AllowableCoefficientIncrease24.00000220.00000RHSValueDual Value8.800000.600000.0000034000.00000120000.00000108000.00000AllowableDecrease88.0000030.00000AllowableIncrease9636.3636416000.00000InfiniteAllowableDecrease4000.0000052000.0000042400.00000(a) What is the optimal solution and the total profit contribution (in $)?DRBDRWtotal 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.Yes, there is no surplus of steel so any additional steel that becomes available should be purchased.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.No, the allowable increase for steel is only 24 pounds, so the additional profits are not applicable for 500 pounds.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.No, there is a slack value of 9,636, so additional pounds of steel will not increase profits.(c) Deegan is considering using overtime to increase the available assembly time. What would you advise Deegan to do regarding this option? Explain.Constraint ? ✓ has a slack. Increasing the number of hours of assembly time will ---Select--- ✓ 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 theoptimal solution? Explain.The objective coefficient range for model DRB shows a lower limit of $Thus, the optimal solution |---Select--- ✓ change and the new value will be $(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 isminutes, so the dual value for this constraint ---Select--- ✓ change.

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acing that pro 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 1,800 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: 200DRB + 280DRW Max s.t. 20DRB + 25DRW 40DRB + 100DRW 60DRB + 40DRW The computer solution is shown below. Variable DRB DRW Constraint 1 2 3 Optimal Objective Value = 371200.00000 Variable DRB DRW DRB, DRW 2 Constraint 1 2 3 ≤ 34,000 Steel available 120,000 ≤ 108,000 Assembly minutes 0 400.00000 1040.00000 Value Reduced Cost 0.00000 0.00000 Slack/Surplus 0.00000 0.00000 42400.00000 Manufacturing minutes Objective Allowable Allowable Coefficient Increase Decrease 200.00000 24.00000 88.00000 280.00000 220.00000 30.00000 RHS Value DRW total profit contribution $ Dual Value 8.80000 0.60000 0.00000 Allowable Increase. 34000.00000 9636.36364 120000.00000 16000.00000 108000.00000 Allowable Decrease 4000.00000 52000.00000 Infinite 42400.00000 (a) What is the optimal solution and the total profit contribution (in $)? DRB (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. O Yes, there is no surplus of steel so any additional steel that becomes available should be purchased. O 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. O No, the allowable increase for steel is only 24 pounds, so the additional profits are not applicable for 500 pounds. O 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. O No, there is a slack value of 9,636, so additional pounds of steel will not increase profits. (c) Deegan is considering using overtime to increase the available assembly time. What would you advise Deegan to do regarding this option? Explain. Constraint ? ✓ has a slack. Increasing the number of hours of assembly time will ---Select--- profits.