The company produces two products, A and B, on two machines, I and II. It has been found that company will realize the profit of $3/unit of Product A and profit of $4/unit of Product B. To produce a unit of Product A needs 6 min on Machine I and 5 min on Machine II. To produce the unit of Product B needs 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift.
a) How many units of every product must be manufactured in every shift to maximize company profit?
b) Determine the optimal profit?