Chapter 3.2, Problem 1E

Formulate but do not solve each of the following exercises as a linear programming problem. You will be asked to solve these problems later.

PRODUCTION SCHEDULING A company manufactures two products, $A$ and $B$, on two machines, $\text{I}$ and $\text{II}$. It has been determined that the company will realize a profit of $\$3$ on each unit of Product $A$ and a profit of $\$4$ on each unit of Product $B$. To manufacture a unit of Product $A$ requires $6\min$ on machine $\text{I}$ and $5\min$ on machine $\text{II}$. To manufacture a unit of Product $B$ requires $9\min$ on Machine $\text{I}$ and $4\min$ on machine $\text{II}$. There are $5\text{hr}$ of machine time available on Machine $\text{I}$ and $3\text{hr}$ of machine $\text{II}$ in each work shift. How many units of each product should be produced in each shift to maximize the company`s profit?