A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $3/unit of Product A and a profit of $6/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a 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?

Question

(x,y)=?

What is the maximum return?

Steve · Answer

maximize p=3x+6y subject to
6x+9y <= 300
5x+4y <= 180

Now just draw the lines and find the vertices. There are many helpful online sites to verify your work. One is at

http://www.zweigmedia.com/RealWorld/LPGrapher/lpg.html