# Formulate a linear programming model to determine the optimal product mix that will maximize profit

A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows.

Hours/Unit

Product Line 1 Line 2

A 12 4

B 4 8

Total Hours 60 40

a. Formulate a linear programming model to determine the optimal product mix that will maximize profit.

b. Transform this model into standard form.

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#### Solution Preview

(a) Let x units of A and y units of B be produced to earn maximum profit. Then we have the linear programming problem:

Maximize P = 9x + 7y

Subject to

12x ...

#### Solution Summary

A neat and step-by-step solution is provided in order to create a linear programming model to maximize profit and then transform this model into standard form.