We are given the following linear programming problem: find the range of optimality for the profit contribution of a medium shelf from the output given above and interpret its meaning.

Mallory furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $200.

The linear programming formulation is

Max 300B + 200M

Subject to

500B + 300 M < 75000

100B + 90M < 18000

B, M > 0

I have solved the problem by using QM for Windows and the output is given below.

The Original Problem w/answers:

B M RHS Dual

Maximize 300 200

Cost Constraint 500 300 <= 75,000 .4667

Storage Space Constraint 100 90 <= 18,000 .6667

Solution-> 90 100 Optimal Z-> 47,000

Ranging Result:

Variable Value Reduced Cost Original Val Lower Bound Upper Bound

B 90. 0 300. 222.22 333.33

M 100. 0 200. 180. 270.

Constraint Dual Value Slack/Surplus Original Val Lower Bound Upper Bound

Cost Constraint 0.4667 0 75000 60000 90000

Storage Space Constraint 0.6667 0 18000 15000 22500

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