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 Industriesmanufactures 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 ofmanufacturing time, and 60 minutes of assembly time. Model DRW requires 25 pounds of the special high alloy steel, 100 minutes ofmanufacturing time, and 40 minutes of assembly time. Deegan's steel supplier indicated that at most 34,000 pounds of the high-alloy steelwill be available next quarter. In addition, Deegan estimates that 2,000 hours of manufacturing time and 1,800 hours of assembly time willbe available next quarter. The profit contributions are $200 per unit for model DRB and $280 per unit for model DRW. The linearprogramming model for this problem is as follows:200DRB + 280DRWMaxs.t.20DRB + 25DRW ≤ 34,00040DRB + 100DRW ≤ 120,000≤ 108,00060DRB + 40DRWDRB, DRW >0The computer solution is shown below.Optimal Objective Value = 371200.00000VariableDRBDRWConstraint123VariableDRBDRWValue400.000001040.00000Slack/SurplusReduced Cost0.000000.000000.000000.0000042400.00000Steel availableManufacturing minutesAssembly minutes200.00000280.00000Objective AllowableCoefficientIncrease24.00000220.00000Dual Value8.800000.600000.00000AllowableDecrease88.0000030.00000 Constraint123VariableDRBDRWConstraint123Slack/Surplus0.000000.0000042400.00000Objective AllowableCoefficientIncrease24.00000220.00000200.00000280.00000RHSValueDual 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 Deeganpurchase 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 thesupplier is offering.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 thatthe 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 9,636, so additional pounds of steel will not increase profits.

(a) The optimal solution is the value marked as "Optimal objective value" in the computer solution…

Answered: (a) What is the optimal solution and…

Practical Management Science

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...

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