Problema Solution
A potter can make a cup in 6 minutes and a plate in 3 minutes. Cups use 3/4 # clay, plates take 1.0 # clay. The potter has 250 # of clay. The potter makes $2.00 profit on each cup and $1.50 on each plate. She has 20 hours to work. How many cups and how many plates should she make to maximize her profit?
Answer provided by our tutors
Let
x = the number of cups, x>0
y = the number of plates, y>0
We have the following constrains:
6x+3y <= 1200 (20 hours = 20*60 = 1200 min )
0.75x+y <= 250
The objective function is the profit F(x, y) = 2x + 1.50y. We need to find the maximum.
First we will find the corner points.
The corner points are: (0, 250), (200, 0), (120, 160)
F(0, 250) = 2*0 + 1.50*250 = $375
F(200, 0) = 2*200 + 1.50*0 = $400
F(120, 160) = 2*120 + 1.50*160 = $480
She should make 120 cups and 160 plates to maximize the profit.