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 $4/unit of Product A and a profit of $5/unit of Product B. To manufacture 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture 1 unit of Product B requires 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. How many units of each product should be produced in each shift to maximize the company's profit? Product A units Product B units What is the largest profit the company can realize? $ Is there any time left unused on the machines? (If so, give the number of minutes remaining. If not, enter 0.) Machine I min Machine II min
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 $4/unit of Product A and a profit of $5/unit of Product B. To manufacture 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture 1 unit of Product B requires 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. How many units of each product should be produced in each shift to maximize the company's profit?
Product A | units |
Product B | units |
What is the largest profit the company can realize?
$
Is there any time left unused on the machines? (If so, give the number of minutes remaining. If not, enter 0.)
Machine I | min |
Machine II | min |
Maximize Z = 4A + 5B |
subject to |
6A + 9B <= 5 hours x 60 minutes |
5A + 4B <= 3 hours x 60 minutes |
A, B >= 0 |
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