A product can be produced on four different machines. Each Machine has a product

Question

A product can be produced on four different machines. Each Machine has a production cost per unit processed and a production capacity (Cap). Using excel solver and LP formulate the model and find the least cost schedule on the machines for the production of   6043 units/day. Be sure to have solver produce the sensitivity report. Then discuss the reduced cost for each decision variable and the shadow price for each constraint. Cost/unit Cap/day Machine1 22 2000 Machine2 29 1876 Machine3 21 1878 Machine4 24 1355 A product can be produced on four different machines. Each Machine has a production cost per unit processed and a production capacity (Cap). Using excel solver and LP formulate the model and find the least cost schedule on the machines for the production of   6043 units/day. Be sure to have solver produce the sensitivity report. Then discuss the reduced cost for each decision variable and the shadow price for each constraint. Cost/unit Cap/day Machine1 22 2000 Machine2 29 1876 Machine3 21 1878 Machine4 24 1355

Explanation / Answer

Total production = 6043 units/ day

Total cost = 22 M1 + 29 M2 + 21 M3 + 24 M4

constraints are

M1 <= 2000

M2 <= 1876

M3 <= 1878

M4 <= 1355

M1 + M2 + M3 + M4 = 6043

Sensitivity Report

Total Cost = $106923

Adjustable Cells Final Reduced Cell Name Value Gradient $C$2 M1 Production 2000 -7 $C$3 M2 Production 810 0 $C$4 M3 Production 1878 -8 $C$5 M4 Production 1355 -29 Constraints Final Lagrange Cell Name Value Multiplier $B$8 TP Cost/Unit 6043 29

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