Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 600 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 200 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Model Regular model Catcher's model Production Time (Hours) Profit/Glove $4 $8 Assuming that the company is interested in maximizing the total profit contribution, answer the following: Cutting and Sewing Finishing 1/2 1 3/2 Max s.t. (a) What is the linear programming model for this problem? If required, round your answers to 3 decimal places or enter your answers as a fraction. If the constant is "1" it must be entered in the box. Do not round intermediate calculation. If an amount is zero, enter "0". Let R= number of units of regular model. C = number of units of catcher's model. X 1.0 X X R R + 1/2 + Packaging and Shipping 1/6 1/2 X₂ + R, C 1.5 c C .5 CS CS S <<<· × Cutting and Sewing Finishing Packing and Shipping

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
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Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 600 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department,
and 200 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table:
Model
Max
Production Time (Hours)
Cutting and
Sewing Finishing
1/2
1
1/2
s.t.
Regular model
Catcher's model
Assuming that the company is interested in maximizing the total profit contribution, answer the following:
(a) What is the linear programming model for this problem? If required, round your answers to 3 decimal places or enter your answers as a fraction. If the constant is "1" it must be entered in the box. Do not round intermediate calculation. If an amount is
zero, enter "0".
3/2
Let R = number of units of regular model.
C = number of units of catcher's model.
.5
1.0
R
R
R
Packaging and
Shipping
1/6
1/2
+
R, C
1.5
.5
X
C
C
с
3c
S
S
C ≤
Profit/Glove
$4
2
$8
Cutting and Sewing
Finishing
Packing and Shipping
Transcribed Image Text:Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 600 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 200 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Model Max Production Time (Hours) Cutting and Sewing Finishing 1/2 1 1/2 s.t. Regular model Catcher's model Assuming that the company is interested in maximizing the total profit contribution, answer the following: (a) What is the linear programming model for this problem? If required, round your answers to 3 decimal places or enter your answers as a fraction. If the constant is "1" it must be entered in the box. Do not round intermediate calculation. If an amount is zero, enter "0". 3/2 Let R = number of units of regular model. C = number of units of catcher's model. .5 1.0 R R R Packaging and Shipping 1/6 1/2 + R, C 1.5 .5 X C C с 3c S S C ≤ Profit/Glove $4 2 $8 Cutting and Sewing Finishing Packing and Shipping
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