# A manager wants to know how many units of each product to produce on a daily basis in order to achieve the highest contribution to profit

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## Description

QUESTION:

A manager wants to know how many units of each product to produce on a daily basis in order to achieve the highest contribution to profit. The production requirements for the products are shown in the following table.

Material 1 costs \$ 5 a pound, material 2 costs \$ 4 a pound, and labor costs \$ 10 an hour. Product A sells for \$ 80 a unit, product B sells for \$ 90 a unit, and product C sells for \$ 70 a unit. Available resources each day are 200 pounds of material 1; 300 pounds of material 2; and 150 hours of labor.

The manager must satisfy certain output requirements: The output of product A should not be more than one- third of the total number of units produced; the ratio of units of product A to units of product B should be 3 to 2; there is a standing order for 5 units of product A each day. Formulate a linear programming model for this problem, and then solve it.

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