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, manyowners 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 aheavier 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 38,000 pounds of the high-alloysteel will be avallable 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.S 38,000 Steel availableS 120,000 Manufacturing minutesS 108,000 Assembly minutes20DRB + 25DRW40DRB + 10ODRW60DRB + 40DRWDRB, DRW 2The computer solution is shown below.Optimal objective Value - 406400.00000VariableValueReduced CoatDRS800.000000.00000DRN0.000000.00000Deal Value8.600000.60000ConstraintSlack/Surplus0.000000.0000024000.00000.00000ALlowableDecreaseAllowableObjectiveCoetticientVariableIncrease200.0000024.000008.00000280.00000220.0000030.00000AllowableDecrease00.0000035428.5714240.0000oAllowableConstraintValueIncrease38000.0000oS636.36364120000.000o32000.0000D108000.00000Infinite (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.O No, the allowable Increase for steel is only 24 pounds, so the additional profits are not applicable for S00 pounds.O No, there is a slack value of 5,636, 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 0 has a slack. Increasing the number of hours of assembly time willSetect--- B profits.(d) Because of increased competition, Deegan is considering reducing the price of model DRB such that the new contribution to profit ia $175 per unit. How would this change in price affect theoptimal solution? Explain.Thus, the optimal solution-elect change and the new value will be sThe objective coefficient range for model DRB shows a lower limit of $(e) If the avalable manufacturing time is Increased by 500 hours, will the dual value for the manufacturing time constraint change? Explain.minutes, so the dual value for this constraint Select B change.The allowable increase isNeed Help?Read

Linear programming is a course of improving the issues which are exposed to specific limitations. It…

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 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 D heavier roll bar that must be weided 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 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 38,000 pounds of the hig steel will be avalable 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 contribution $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 + 28ODRW s.t. S 38,000 Steel avalable 40DRB + 100DRW S 120,000 Manufacturing minutes 60DRB + 40DRW S 108,000 Assembly minutes 20DRB + 25DRW DRB, DRW 2 The computer solution is shown below. Optimal Objective Value - 40400.c0000 Variable Value Reduced Coat DRS B00.00000 0.00000 DRN 0.00000 0.00000 Constraint Slack/Surplus Dual Value 0.00000 0.00000 0.60000 24800.00000 0.00000 Allowable ALlowable Cbjective Coetticient Variable Increase Decrease .00000 30.00000 D 200.00000 24.00000 280.00000 220.00000 Allowable Decrease Allowable Conat.caint. Value Increase

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...