## 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

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. Production requirements for the products are shown in the following table. Product Material 1 (pounds) Material 2 (pounds) Labor (hours) A 2 3 3.2 B 1 5 1.5 C 6 ?? 2.0 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; and there is a standing order for 5 units of product A each day. Formulate a linear programming model for this problem, and then solve.

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