Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a
ID: 388554 • Letter: K
Question
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 1200 hours of production time available in its cutting and sewing department, 250 hour available in its finishing department, and 120 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table Production Time (hours) Cutting and Sewing Packaging and Shipping Finishing Profit/Glove Model Regular model Catcher' s model $11 Letting R -number of regular gloves C number of catcher's mitts leads to the following formulation: Max 8R 11c s.t. 2R+2C 1200 R+, CS 250 Cutting and sewing Finishing Packaging and shippingExplanation / Answer
a.
b.)
As long as the profit per regular glove is between 6.87500 and 13.75000 the optimal solution of number of each gloves will not change.
As long as the profit per catcher glove is between 6.40000 and 12.80000 the optimal solution of number of each gloves will not change.
The assumption is that both coeffiecient are not changed at the same time.
c.)
As long as the number of hours available for cutting and sewing are within the above range the change in the optimal value of the solution per unit increase in the right hand side of the constraint is 0.
As long as the number of hours available for finishing are within the above range the change in the optimal value of the solution per unit increase in the right hand side of the constraint is 4.50000.
As long as the number of hours available for Packaging are within the above range the change in the optimal value of the solution per unit increase in the right hand side of the constraint is 46.00000.
d.)
How much will the value of optimal solution will improve 3 extra hours of packaging and shipping are made available?
Answer: The optimal solution will improve by $138.
New optimal solution= Current solution + (Dual price)*(Change in right hand side)
= 6645 + 46*3 = 6783
The improvement is = 46*3 = $138
Objective coefficient range Variable Lower limit Upper liimit Regular glove 6.87500 13.75000 Catcher's mitt 6.40000 12.80000Related Questions
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