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 2C ≤ 800 Cutting and sewing 1 2R + 1 3C ≤ 240 Finishing 1 8R + 1 4C ≤ 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.) 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 10 extra hours of packaging and shipping time are made available?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section: Chapter Questions

Problem 31P

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Question

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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

s.t.

≤

800

Cutting and sewing

≤

240

Finishing

≤

100

Packaging and shipping

≥ 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.)

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 10 extra hours of packaging and shipping time are made available?

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