# Linear Programming

We are given the following linear programming problem:

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. I don't know what it mean though. Can you help me with this. I only need to answer one of the question below. Can you tell me how to go about figuring that information out?

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

1. Determine and interpret the optimal solution and optimal objective function value from the output given above.

2. Find the range of optimality for the profit contribution of a big shelf from the output given above and interpret its meaning.

3. Find the range of optimality for the profit contribution of a medium shelf from the output given above and interpret its meaning.

4. Find the range of feasibility for the right hand side value (availability) of money constraint from the output given above and interpret its meaning.

5. Find the range of feasibility for the right hand side value (availability) of storage space constraint from the output given above and interpret its meaning.

6. Determine and interpret the shadow (dual) prices of the two resources.

#### Solution Summary

The Correct Solution is Provided. Only Question 1 has been answered in this posting as required.