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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.

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