A company manufactures two products, A and B, on two machines. I and II. It has been determined that the company will realize a profit of $3/unit on produce A, and a profit of $4 unit on product B. To manufacture 1 unit of product A requires 6 mins on Machine I and 5mins on Machine II. To manufacture I unit of B requires 9 mins on machine I and 4 mins on machine II. There are 5 hr of machine time available on machine I and 3 hr of machine time available on machine II. How many units of each product should be produced in each shift to maximize the company's profit? What is the largest profit the company can realize? Is there any time left unused on the machines