We are given the following linear programming problem: Mallory furniture buys 2
ID: 3120989 • Letter: W
Question
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.
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
Determine and interpret the shadow (dual) prices of the two resources:
Explanation / Answer
1.
The range of feasibility of the accessibility of storage space is from the lower bound to the upper bound. Thus, between 15000 and 22500 cubic feet, it adds a value of 0.6667 per cubic feet if use for also Big or Small Shelves. This The value of each cubic foot of storage space.