# Linear Programming Model: A Clothier Making Coats and Slacks

Please help with the following problem.

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, whereas 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.

Formulate a linear programming model for this program.

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#### Solution Preview

Decision variables:

Let the number of coats produced be x1 and number of slacks produced x2

Objective function:

The objective is to maximize profits

The profit for a coat is $50, and the profit for slacks is $40

Therefore, the objective function is

Maximize ...

#### Solution Summary

A linear programming model is formulated for the clothier making coats and slacks, including the decision variables, object functions and constraints.