krm8_ism_e - Supplement E Linear Programming DISCUSSION...

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Supplement E Linear Programming DISCUSSION QUESTION Overtime would relax the labor constraint, but the additional labor resource comes at a cost. Would additional labor hours improve the solution at a rate sufficient to pay for overtime? If so, how many additional hours would be of value? Which of the other resources would then bind the solution? In what way would the decision change if additional labor is made available? Storage space is not a binding constraint in the optimal solution. The linear programming model would show that the shadow price for storage is zero. No amount of rent to obtain additional storage can be justified. PROBLEMS 1. Really Big Shoe Definition of decision variables: X 1 = number of basketball teams sponsored X 2 = number of football teams sponsored a. Objective function and constraints Maximize: 1 1 1 2 X X + Subject to: 1) money: $1, , $300, $30, , 000 000 000 000 000 1 2 X X + 2) flubber: ( 29 ( 29 1 2 3 32 1 120 4,000 X X + 1 2 , 0 X X
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147 l PART 3 l Managing Value Chains b. Graphical analysis. The optimal solution occurs at point B. c. The optimal solution at point B occurs at the intersection of the money and flubber constraints. This appears to be at coordinates (26, 14). To algebraically find the intersection of the money and flubber constraints, we multiply the money constraint by 0.0004, then subtract the flubber constraint from the money constraint. 1 2 1 2 1 400 120 12,000 96 120 4,000 304 8,000 X X X X X + = - - = - = X 1 26 3 = . or 26 basketball teams 400 26 120 12 000 120 1600 1333 2 2 2 ( 29 + = = = X X X , , . or 13 football teams 2. Nowledge College (minimize hours of study) Definition of decision variables: X 1 = number of business courses X 2 = number of nonbusiness courses a. Objective function and constraints Minimize: 120 200 1 2 X X +
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Linear Programming l SUPPLEMENT E l 148 Subject to: 1) money: $60 $24 $3, X X 1 2 000 + 2) business: 1 1 23 X 3) nonbusiness: 2 1 20 X 4) total courses: 1 2 1 1 65 X X + 1 2 , 0 X X b. Graphic analysis. Feasible region is defined by points A, B, and C. c. Optimal solution is at point C, where X 1 40 = and X 2 25 = . d. Neither the number of business classes nor number of nonbusiness classes is binding the optimal solution. There are 17 units of surplus in the constraint on business classes and 5 units of surplus in the constraint for the number of nonbusiness courses. These conclusions are confirmed by the Linear Programming Solver :
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149 l PART 3 l Managing Value Chains Variable Variable Original Coefficient Label Value Coefficient Sensitivity X1 40.0000 120.0000 0 X2 25.0000 200.0000 0 Constraint Original Slack or Shadow Label RHV Surplus Price money 3,000 0 business 23 -17 0 nonbusiness 20 -5 0 total courses 65 0 253.3333 Objective Function Value: 9,800 3. Nowledge College (minimize cost of books) Definition of decision variables: X 1 = number of business courses X 2 = number of nonbusiness courses a. Objective function and constraints Minimize: 1 2
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This note was uploaded on 12/19/2009 for the course MANAGEMENT 00123 taught by Professor Ahmed during the Spring '09 term at Albany College of Pharmacy and Health Sciences.

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krm8_ism_e - Supplement E Linear Programming DISCUSSION...

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