G. Managerial Economics Applications of Linear Programming. Information about a version of the make-buy problem discussed in class and on an assignment is attached. [20 Points] G.1 Briefly explain the decision variables, objective function and constraints for the problem. G.2 Interpret the optimal solution to the linear program. A Make-Buy Problem The following application of linear programming to a production problem is from Spreadsheet Modeling and Decision Analysis by Cliff T. Ragesdale. Electro-Poly Corporation supplies three types of slip rings to industrial customers. The quantity of each type of slip ring which will be delivered in the next planning period is fixed set by contracts with the purchasers. Production is limited by available wiring and harnessing capacity. Sales in excess of the firm’s production may be met by purchasing the necessary quantities. In the next production period, the firm will deliver 500 units of model A, 1,350 units of model B, 3,000 units of model C, and 4,500 units of model D. There are 6,000 hours of wiring time available and 3,500 hours of harnessing time. The price per unit for variable inputs is $6.31 for materials 1 and $4.25 for materials 2. Since other variable costs are measured in dollars, use a price of $1.00 The following tableau shows how the firm’s cost minimization problem can be modeled as a linear program, where XMj is the number of type j slip rings made, XBj is the number of type j slip rings bought, CMi is the variable cost per unit for producing product j, and the objective function and constraints are as discussed in class : Variable Cost | CMA | CMB | ___ | CMD | 116.7 | 128.0 | 88.3 | 62.0 T ring Time, Hr arnessing Type RHS S 6,000 S 3,500 500 21,350 2 3,000 2 4,500 0.97 0.980.500.64 Time, Hr 0.48 0.33 0.62 0.35 of Model A of Model B of Model C of Model D Excel Model with Solver Results Electro-Poly Corporation: A Buy-Make Decision Problem Slip Ring Model A Model B Model C Model D Units to Make 0.0 1,350.0 2,386.3 4,500.0 613.7 Units to Buy 500.0 0.0 0.0 Variable Input Requirement per Unit Input Price $6.31 Materials 2 $4.25 Other Variable Costs $1.00 Model A 8.49 8.07 16.07 $103.94 Model B 9.60 7.73 8.45 $101.88 Model C 1.56 10.78 10.73 $66.39 Model D 1.38 6.53 4.64 $41.10 Materials 1 Per Unit Variable Cost to Make Total Cost Unit Cost to Buy $116.70 $128.00 $88.30 $62.00 $593,450 Model A Model B 1,350 1,350 Model C 3,000 3,000 Model D Total Number Made & Bought 500 4,500 Number Needed 500 4,500 Fixed Input Requirement per Unit Input Model A Model B Model C Model D Use Available Wiring, Hr 0.97 Harnessing, Hr 0.48 0.98 0.50 0.64 5,396.1 6,000.0 0.33 0.62 0.35 3,500.0 3,500.0 Based on an example from Spreadsheet Modeling and Decision Analysis by Cliff T. Ragesdale Microsoft Excel 14.0 Answer Report ective Cell (Min Cell Name Final Value $593,450 $H$16 Unit Cost to Buy Total Cost Variable Cells Cell Name $C$7 Units to Make Model A SD$7 Units to Make Model B $ES7 Units to Make Model C SF$7 Units to Make Model D SC$8 Units to Buy Model A SD$8 Units to Buy Model B SES8 Units to Buy Model C SF$8 Units to Buy Model D Final Value 1,350.0 2,386.3 4,500.0 500.0 613.7 Constraints Cell Name $C$19 Total Number Made & SD$19 Total Number Made & ES19 Total Number Made & SF$19 Total Number Made & $G$24 Wiring, Hr Use $G$25 Hamessing, Hr Use Cell Value Formula Status Slack ht Model A t Model B t Model C t Model D 500.0 SC$19 $C$20 Bin 1,350.0 SD$19-$D$20 Bin 3,000.0 SE$19 SE$20 Bin 4,500.0 SFS19-$F$20 Bin 5,396.1 $G$24 $H$24 Not Binding 603.85 3,500.0 $G$25<-$H$25 Binding 0.00 Microsoft Excel 14.0 Sensitivity Report Variable Cells Final Reduced Objective Cost Coefficient 103.939 101.879 66.389 Cell SC$7 SDS7 SE$7 $F$7 SC$8 SDS8 SE$8 $F$8 Name Units to Make Model A Units to Make Model B Units to Make Model C Units to Make Model D Units to Buy Model A Units to Buy Model B Units to Buy Model C Units to Buy Model D Value 1350.0 2386.3 4500.0 500.0 4.203 0.000 0.000 0.000 0.000 14.459 0.000 116.700 128.000 88.300 62.000 Constraints Cell SC$19 $D$19 $E$19 SF$19 SG$24 SG$25 Name Total Number Made & Bought Model A Total Number Made & Total Number Made & Total Number Made & Wiring, Hr Use Harnessing, Hr Use Final Value 500.00 1350.00 3000.00 4500.00 5396.15 3500.00 Shadow Constraint Price R.H. Side 500 1350 3000 4500 6000 3500 116.70 ht Model B ht Model C ht Model D 88.30 35.34
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