1. The Grand Valley Company, run by the. Motwani family, produces two products:

Question

1. The Grand Valley Company, run by the. Motwani family, produces two products: bed mattresses and box springs. A prior contract requires that the firm produce at least 30 mattresses or box springs, in any combination, per week. In addition, union labor agreements demand that stitching machines be kept running at least 40 hours per week, which is one production period. The firm plans to purchase four machines. Each box spring takes 2 hours of stitching time, while each mattress takes 1 hour on the machine. The firm believes that it can sell at least twice as much mattresses as box springs. Each mattress produced cost $20 and each box spring costs $24 Formulate this problem as a linear programming problem

Explanation / Answer

X1- Bad mattresses

X2-Boxsprings

X1+X2>=30

2X1+X2>=40

X2=2X1

Min Z=20X1+24X2

therefore,

LPP

min Z=20X1+24X2

sub to constrain,

X1+X2>=30

2X1+X2>=160

x2>=2X1

X2-2X1>=0

x1, x2>0

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