Chapter 4.CRE, Problem 23CRE

MAXIMIZING PROFIT A company manufactures three products, $A,B,\text{and}C$, on two machines, I and II. It has been determined that the company will realize a profit of $\$4/\text{unit}$ of Product $A$, $\$6/\text{unit}$ of Product $B$, and $\$8/\text{unit}$ of Product $C$. Manufacturing a unit of Product $A$ requires $9$ min on Machine I and $6$ min on Machine II; manufacturing a unit of Product $B$ requires $12$ min on Machine I and $6$ min on Machine II; manufacturing a unit of Product $C$ requires $18$ min on Machine I and $10$ min on Machine II. There are $6$ hr of machine time available on Machine I and $4$ hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company’s profit? What is the maximum profit?