Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a
ID: 389336 • 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 700 hours of production time available in its cutting and sewing department 300 hours available in its finishing department, and 100 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 Model Regular model Catcher s model 10 $10 R number of regular gloves C-number of catcher's mitts leads to the following formulation: Max 7R + 10C s.t. R + 10 700 Cutting and sewing /R Cs 300 Finishing BR + %CS 100 Packaging and shipping The sensitivity report is shown in figure below. Optimal Objective Value 4400.00000 Variable Value Reduced Cost 575,00000 0.00000 0.00000 37.50000 Constraint Slack/Surplus Dual Value 0.00000 0.00000 20.62500 2.00000 10.00000 0.00000 Objective Coefficient 7.00000 10.00000 Allowable Increase Allowable Decrease Variable 8.00000 13.33330 4.00000 5.33330 RHS Allowable Allowable ConstraintExplanation / Answer
Part A.
lower limit = value – allowable decrease in value
Upper limit = value + allowable increase in value
Glove
Coefficient value
Allowable decrease
Allowable increase
Lower Limit
Upper limit
R
7
4
8
7-6
= 3
7+8
= 15
C
10
5.33
13.33
4.67
23.33
b.
As long as the profit per regular glove is within limit the optimal solution of regular gloves will not change.
Or as long as the profit per catcher glove is within limit the optimal solution of catcher’s mitt gloves will not change.
The assumption is that single variable coefficient changed at the same time.
c.
Glove
Coefficient value
Allowable decrease
Allowable increase
Lower Limit
Upper limit
Cutting and Sewing
700
100
471.43
600
1171.43
Finishing
300
230
50.0
70
370
Packaging
100
20.63
unlimited
79.37
unlimited
The dual value or shadow price is the change in the objective function if the RHS of the constraint is changed by one unit.
Shadow price of constraint 1 = 2, thus the objective function will increase by $2 if the RHS of constraint is increased by one unit.
As long as the number of hours available for cutting and sewing (constraint 1) are within limit the change in the optimal value of the solution per unit increase in the RHS of the constraint is 2.
As long as the number of hours available for finishing (constraint 2) are within limit the change in the optimal value of the solution per unit increase in the RHS of the constraint is 10.
As long as the number of hours available for packaging (constraint 3) are within limit the change in the optimal value of the solution per unit increase in the RHS of the constraint is 0. Since it is not binding constraint.
d.
Since packaging constraint is not binding constraint, even if extra unit is made available the objective function value will not change.
Amount: $0
Glove
Coefficient value
Allowable decrease
Allowable increase
Lower Limit
Upper limit
R
7
4
8
7-6
= 3
7+8
= 15
C
10
5.33
13.33
4.67
23.33
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