A clothier makes coats and slacks. The two resources required are wool cloth and labor. The clothier has 150 square yards of wool and 200 hours of labor available. Each coat requires 3 square yards of wool and 10 hours of labor. Each pair of slacks requires 5 square yards of wool and 4 hours of labor. The profit for a coat is $50, and the profit for slacks is $40. The clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized. a. Give the Objective function.
b. Give the constraints
c. Graph the solution
d. Give the optimal Point

a. Give the Objective function.

Let c = #coats to be produced

Let s = #slacks to be produced

b. Give the constraints

3c+5s≤150

10c+4s≤200

d. Give the optimal Point

The profit function would be P(x,y)=50c+40s

Explanation:

Let c = #coats to be produced

Let s = #slacks to be produced

Our first constraint deals with square yards of wool. We cannot exceed 150 square yards. Using the fact that coats require 3 sq yds and slacks require 5 sq yds, we can identify this constraint.

3c+5s≤150

Our second constraint deals with the number of hours available being 200. Coats require 10 hrs and slacks require 4 hrs. Now we have our second constraint.

10c+4s≤200

We might also assume that some of each will be produced, so we can list the following as constraints as well.

c>0 and s>0

The profit function would be P(x,y)=50c+40s

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