A factory manufactures two products, A and B. Each product requires the use of three machines, Machine I, Machine II, and Machine III. The time requirements and total hours available on each machine are listed below.

If product A generates a profit of $55 per unit and product B a profit of $40 per unit, how many units of each product should be manufactured to maximize profit, and what is the maximum profit?

Product A Product B Total Hours Machine I Machine II Machine III 1 2 4 2 2 2 74 94 172