Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a
ID: 467869 • 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 hours 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:
I have seen multiple questions about this type of question, but I am not able to understand. I have seen the formulas but if you could answer and explain them to me, that would be fantastic. Thank you.
Explanation / Answer
a)
From above table, objective coefficient range for regular glove is 8
allowable increase is 5.75 , it means that the maximum value of objective coefficient for regular glove should be 8+5.75 = 13.75 so that optimal value of solution doesn't change.
allowable decrease is 1.125 , it means that the minimum value of objective coefficient for regular glove should be 8-1.125 = 6.875 so that optimal value of solution doesn't change.
objective coefficient range for catcher's Mitt is 11
allowable increase is 1.8 , it means that the maximum value of objective coefficient for catcher's Mitt should be 11+1.8 = 12.8 so that optimal value of solution doesn't change.
allowable decrease is 4.6 , it means that the minimum value of objective coefficient for catcher's Mitt should be 11-4.6 = 6.4 so that optimal value of solution doesn't change.
b)
As long as the profit per regular glove is between 6.675 and 13.75, the optimal solution of 40 for regular glove and 575 for catcher glove will not change.
As long as the profit per Catcher glove is between 6.4 and 12.8, the optimal solution of 40 for regular glove and 575 for catcher glove will not change.
assumption is that range of optimality will remain same
c)
From above table,Right hand side value for cutting and sewing is 1200
allowable increase is infinite , it means that the maximum value of right hand side for cutting and sewing should be N/A
allowable decrease is 257.5 , it means that the minimum value of right hand side for cutting and sewingshould be 1200-257.5 = 942.5 so that optimal value of solution doesn't change.
Right hand side value for finishing is 250
allowable increase is 60.588 , it means that the maximum value of right hand side for finishing should be 250+60.588 = 310.588
allowable decrease is 10 , it means that the minimum value of right hand side for finishing should be 250-10 = 240
Right hand side value for packaging is 120
allowable increase is 5 , it means that the maximum value of right hand side for packaging should be 120+5 = 125
allowable decrease is 57.5 , it means that the minimum value of right hand side for packaging should be 120-57.5 = 62.5
As long as the no. of hour for cutting and sewing is above 942.5 the change in optimal value of the solution per unit increase in the right - hand side of the constraint is 0
As long as the no. of hour for finishing is between 240 and 310.588 the change in optimal value of the solution per unit increase in the right - hand side of the constraint is $4.5
As long as the no. of hour for packaging is between 62.5 and 125 the change in optimal value of the solution per unit increase in the right - hand side of the constraint is $ 46
d) if 3 extra hours of packaging and shipping time are made available then optimal solution will improve by 3* 46 = $138. In this case the change will per unit value of dual price.
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