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 ≤ 800 Cutting and sewing

1/2 R + 1/3 C ≤ 240 Finishing

1/8 R + 1/4 C ≤ 100 Packaging and shipping

R, C ≥ 0

The computer solution is shown below.

Optimal Objective Value = 3520.00000

Variable Value Reduced Cost

R 320.00000 0.00000

C 240.00000 0.00000

Constraint Slack/Surplus Dual Value

1 120.00000 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

1 800.00000 Infinite 120.00000

2 240.00000 160.00000 106.66667

3 100.00000 24.00000 40.00000

(a) Determine the objective coefficient ranges. (Round your answers to two decimal places.)

regulars 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 (is/is not) optimal. As long as the profit contribution for the catcher's mitt is between $_______ and $ _______, the current solution (is/is not) 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.)

current and sewing _______ to __________

finishing _________ to ____________

packaging and shipping ______ to _________

(d)

How much will the value of the optimal solution improve (in $) if 10 extra hours of packaging and shipping time are made available?