Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting

R = number of regular gloves
C = number of catcher's mitts

leads to the following formulation:
Max 5R + 8C
s.t.
R +
3
2
C ≤ 1,000 Cutting and sewing

1
2
R +
1
3
C ≤ 260 Finishing

1
8
R +
1
4
C ≤ 100 Packaging and shipping
R, C ≥ 0
The computer solution is shown below.
Optimal Objective Value = 3580.00000
Variable Value Reduced Cost
R 380.00000 0.00000
C 210.00000 0.00000
Constraint Slack/Surplus Dual Value
1 305.00000 0.00000
2 0.00000 3.00000
3 0.00000 28.00000
Variable Objective
Coefficient Allowable
Increase Allowable
Decrease
R 5.00000 7.00000 1.00000
C 8.00000 2.00000 4.66667
Constraint RHS
Value Allowable
Increase Allowable
Decrease
1 1000.00000 Infinite 305.00000
2 260.00000 140.00000 126.66667
3 100.00000 61.00000 35.00000
(a)
Determine the objective coefficient ranges. (Round your answers to two decimal places.)
regular glove to catcher's mitt to
(b)
Interpret the ranges in part (a). (Round your answers to two decimal places.)
As long as the profit contribution for the regular glove is between $ and $ , the current solution
optimal. As long as the profit contribution for the catcher's mitt is between $ and $ , the current solution
optimal.
(c)
Interpret the right-hand-side ranges.
The dual values for the resources are applicable over the following ranges. (Round your answers to two decimal places. If there is no upper or lower limit, enter NO LIMIT.)
cutting and sewing
to
finishing
to
packaging and shipping
to
(d)
How much will the value of the optimal solution improve (in $) if 20 extra hours of packaging and shipping time are made available?
$