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 DR8 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 32,000 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: Max200DRB+280DRWs.t.20DRB+25DRW32,000Steelavailable40DRB+1000RW120,000Manufacturingminutes60DRB+40DRW108,000Assemblyminutes The computer solution is shown below. Optimalobjectivevalue=353600,00000 (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 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, 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 11,636 , 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 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 $ change and the new value will be $ x. . Thus, the optimal solution (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 x minutes, so the dual value for this constraint change
