(a) What is the linear programming model for this problem? (Assume R is the number of units of regular model gloves and C is the number of units of catcher's model gloves.) Max        s.t.cutting and sewing       finishing       packaging and shipping       R, C ≥ 0 (b) Find the optimal solution using the graphical solution procedure. How many gloves of each model should Kelson manufacture? regular model glovescatcher's model gloves (c) What is the total profit contribution (in dollars) Kelson can earn with the given production quantities?

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 890 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.

Model Production Time
(hours)
Cutting and Sewing Finishing Packaging and
Shipping
Profit/Glove
Regular model 1
1
2
1
8
$4
Catcher's model
3
2
1
3
1
4
$7
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? (Assume R is the number of units of regular model gloves and C is the number of units of catcher's model gloves.)
Max 
 
 
 
s.t.cutting and sewing
 
 
 
finishing
 
 
 
packaging and shipping
 
 
 
R, C ≥ 0
(b)
Find the optimal solution using the graphical solution procedure. How many gloves of each model should Kelson manufacture?
regular model glovescatcher's model gloves
(c)
What is the total profit contribution (in dollars) Kelson can earn with the given production quantities?
(d)
How many hours of production time will be scheduled in each department?
cutting and sewing hoursfinishing hourspackaging and shipping hours
(e)
What is the slack time (in hours) in each department?
cutting and sewing hoursfinishing hourspackaging and shipping hours
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ISBN:
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Cengage,