A manufacturer of outdoor clothing makes wax jackets and trousers. Each jacket requires 1 hour to whereas each pair of trousers takes 40 minutes. The materials for a jacket cost $32 and those for a p trousers cost $40. The company can devote only 34 hours per week to the production of jackets and trou and the firm's total wooldu

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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A manufacturer of outdoor clothing makes wax jackets and trousers. Each jacket requires 1 hour to make,
whereas each pair of trousers takes 40 minutes. The materials for a jacket cost $32 and those for a pair of
trousers cost $40. The company can devote only 34 hours per week to the production of jackets and trousers,
and the firm's total weekly cost for materials must not exceed $1200. The company sells the jackets at a profit
of $12 each and the trousers at a profit of $14 per pair. Market research indicates that the firm can sell all of
the jackets that are produced, but that it can sell at most half as many pairs of trousers as jackets. The
feasible region as well as the constraints associated to the linear programming problem above can be seen in
the Figure
25
y
20
15
10
5
0 B
0
5
10
15
XM0
y≥ 0
32x + 40y≤ 1200
x+2/3y ≤ 34
x/2 ≤y
A
20 25
D
X
✓in this problem must be
30
The objective function
the problem is
can be achieved if the manufacturer arranges the production as
CH
35
v. We know that the solution to
of the feasible region. Therefore, the maximum profit $
Transcribed Image Text:A manufacturer of outdoor clothing makes wax jackets and trousers. Each jacket requires 1 hour to make, whereas each pair of trousers takes 40 minutes. The materials for a jacket cost $32 and those for a pair of trousers cost $40. The company can devote only 34 hours per week to the production of jackets and trousers, and the firm's total weekly cost for materials must not exceed $1200. The company sells the jackets at a profit of $12 each and the trousers at a profit of $14 per pair. Market research indicates that the firm can sell all of the jackets that are produced, but that it can sell at most half as many pairs of trousers as jackets. The feasible region as well as the constraints associated to the linear programming problem above can be seen in the Figure 25 y 20 15 10 5 0 B 0 5 10 15 XM0 y≥ 0 32x + 40y≤ 1200 x+2/3y ≤ 34 x/2 ≤y A 20 25 D X ✓in this problem must be 30 The objective function the problem is can be achieved if the manufacturer arranges the production as CH 35 v. We know that the solution to of the feasible region. Therefore, the maximum profit $
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