Question

a manufacturer of tennis rackets makes a profit of $15 on each set point racket and $8 on each double fault racket. to meet dealer demands, daily production of double faults should be between 30 and 80, where as the number of set points should be between 10 and 30. in order to maintain high quality, the total number of rackets produced shouldn't exceed 80 per day. how many of each type should be manufactured to maximize profit?

Answer 1

Let S be the number of set point racquets made, D be double fault.

Then profit = 15S + 8D and S + D <= 80

Max profit when S, D as large as possible, i.e. S + D = 80

Answer 2

i don't get it .

Answer 3

Sorry. Draw the graph of S + D >= 80

It's a straight line of negative slope, with x and y intercepts of 80 (S is the x-axis, D is the y-axis).

Now the POSSIBLE combinations of S and D are all inside or on that line.

The MAXIMUM combination of S and D is a point on the line

Can you see how to find the point on the line where profit is as maximum?

Answer 4

Another hint. The possible region is also limited by the constraints on D (>30, <80) and S (>10, <80), so the only possibilities are on the line between (10,70) and (30,50)