. 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. Product Hours/Unit 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.

(a) Linear model

Subject to:

(b) Standard form:

Subject to:

Explanation:

Given

Solving (a): Formulate a linear programming model

From the question, we understand that:

A has a profit of $9 while B has $7

So, the linear model is:

Subject to:

Where:

Solving (b): The model in standard form:

To do this, we introduce surplus and slack variable "s"

For inequalities, we add surplus (add s)

Otherwise, we remove slack (minus s)

So, the standard form is:

So, the linear model is:

Subject to: