A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits. Production requirements for the products are shown in the following table. Product Material 1 (lbs.) Material 2 (lbs.) 3 1 5 4 none Labor (hours) 2 3.5 Material 1 costs $7 a pound, material 2 costs $5 a pound, and labor costs $15 per hour. Product A sells for $101 a unit, product B sells for 567 a unit, and product C sells for $97.50 a unit. Each week there are 300 pounds of material 1; 400 pounds of material 2; and 200 hours of labor. Also, there is a weekly demand of 10 units of product C each week.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 56P
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LINEAR PROGRAMMING PROBLEM
27. A production manager wants to determine how many units of each product to produce weekly to
maximize weekly profits. Production requirements for the products are shown in the following
table.
Product Material 1 (lbs.) Material 2 (lbs.)
A
B
C
3
1
5
2
4
none
Labor (hours)
2
3.5
Material 1 costs $7 a pound, material 2 costs $5 a pound, and labor costs $15 per hour. Product
A sells for $101 a unit, product B sells for 567 a unit, and product C sells for $97.50 a unit. Each
week there are 300 pounds of material 1; 400 pounds of material 2, and 200 hours of labor.
Also, there is a weekly demand of 10 units of product C each week.
Transcribed Image Text:LINEAR PROGRAMMING PROBLEM 27. A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits. Production requirements for the products are shown in the following table. Product Material 1 (lbs.) Material 2 (lbs.) A B C 3 1 5 2 4 none Labor (hours) 2 3.5 Material 1 costs $7 a pound, material 2 costs $5 a pound, and labor costs $15 per hour. Product A sells for $101 a unit, product B sells for 567 a unit, and product C sells for $97.50 a unit. Each week there are 300 pounds of material 1; 400 pounds of material 2, and 200 hours of labor. Also, there is a weekly demand of 10 units of product C each week.
A
1 Problem 27
2
3
4 Number of Units
5 Revenue
6 Material cost
7 Labor cost
8 Profit
9 Constraints
10
GEEREE
11
12
13
14
15
B
C
Produce A Prodcut B
D
Product C
E
LHS
F
G
Sign RHS
H
Cost
Transcribed Image Text:A 1 Problem 27 2 3 4 Number of Units 5 Revenue 6 Material cost 7 Labor cost 8 Profit 9 Constraints 10 GEEREE 11 12 13 14 15 B C Produce A Prodcut B D Product C E LHS F G Sign RHS H Cost
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