Question: Use the simplex method to solve the linear programming problem. MAXIMIZING PROFIT A company manufactures three products, A, B, and C, on two machines, I and II. It has been determined that the company will realize a profit of $4/unit of product A, $6/unit of product B, and $8/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 in order to maximize the company's profit?