A company manufactures x units of
Product A and y units of
Product B, on two machines, I and II. It has been
determined that the company will realize a profit
of $2 on each unit of
Product A and $4 on each unit of
Product B. To manufacture a unit of
Product A requires 5 min on Machine I
and 3 min on Machine II. To manufacture a unit of
Product B requires 8 min on Machine I
and 5 min on Machine II. There are 256 min
available on Machine I and 157 min available on Machine
II in each work shift. How many units of a product should be
produced in each shift to maximize the company's
profit P in dollars?