Ch3 Solution 18

Ch3 Solution 18 - desirable. e. Because constraint 4 is not...

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Chapter 3 Linear Programming: Sensitivity Analysis and Interpretation of Solution 18. a. The linear programming model is as follows: Min 30AN + 50AO + 25BN + 40BO s.t. AN + AO 50,000 BN + BO 70,000 AN + BN 80,000 AO + BO 60,000 b. Optimal solution: New Line Old Line Model A 50,000 0 Model B 30,000 40,000 Total Cost $3,850,000 c. The first three constraints are binding because the values in the Slack/Surplus column for these constraints are zero. The fourth constraint, with a slack of 0 is nonbinding. d. The dual value for the new production line capacity constraint is -15. Because the dual value is negative, increasing the right-hand side of constraint 3 will cause the objective function value to decrease. Thus, every one unit increase in the right hand side of this constraint will reduce the total production cost by $15. In other words, an increase in capacity for the new production line is
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Unformatted text preview: desirable. e. Because constraint 4 is not a binding constraint, any increase in the production line capacity of the old production line will have no effect on the optimal solution. Thus, there is no benefit in increasing the capacity of the old production line. f. The reduced cost for Model A made on the old production line is 5. Thus, the cost would have to decrease by at least $5 before any units of model A would be produced on the old production line. g. The right hand side range for constraint 2 shows an allowable decrease of 20,000. Thus, if the minimum production requirement is reduced 10,000 units to 60,000, the dual value of 40 is applicable. Thus, total cost would decrease by 10,000(40) = $400,000....
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This note was uploaded on 05/01/2011 for the course BUS 220 taught by Professor Drexel during the Fall '08 term at SUNY Stony Brook.

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