Question

PLEASE HELP!!!!!

A product Using excel solver and LP formulate the model and find the least cost schedule on the machines for the productior 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. can be produced on four different machines. Each Machine has a production cost per unit processed and a production capacity (Cap) 2984 units/day. Cost/unit Cap/day Machine1 24 1066 Machine2 Machine3 Machine4 27 1671 15 1194 15 1415

Answer 1

Decision variables are number of units produced on four different machines.

i.e., X₁ for Machine1,    X₂ for Machine2,    X₃ for Machine3 and  X₄ for Machine4.

Then, objective function   

Zmin24X127 X2+ 15X3 + 15X4

and constraints

X1X2X3+ X4 =2984

X11066

X2 1671

X3 194

X4 1415

and   

X120, X2 0, X30, X40

Then, by Excel solver,

	x1	x2	x3	x4	Total	Max. Capacity
Decision variable value	1066	1671	0	345
Cost/Unit	24	27	15	15	75876
cap/day machine 1	1	0	0	0	1066	1066
cap/day machine 2	0	1	0	0	1671	1671
cap/day machine 3	0	0	1	0	0	1194
cap/day machine 4	0	0	0	1	345	1415
production per day	1	1	1	1	3082	3082

Where,

Solver Parameters $G$4 Set Target Cell: Solve Equal To: 0 Value of: Max Min Close By Changing Cells: $C$3:$F$3 Guess Subject to the Constraints: Options $G$10 $H$10 $G$6 <$H$6 $G$7 <=$H$7 Add Change 8$H$=> 8$$ 6$H$ > 6$5$ Reset All Delete Help HA

Hence,

Machine1 Cap/day X₁ = 1066 units/day

Machine2 Cap/day X₂ = 1671 units/day

Machine3 Cap/day X₃ = 0 units/day

Machine4 Cap/day X₄ = 345 units/day

and   the least cost schedule on the machines for the production of 2940 units/day is 75876.