Q:

Aurelia makes and sells ceramic cups and plates. It takes her 10 minutes to make a cup and 20 minutes to make a plate. Each cup uses 3 pounds of clay and each plate uses 2 pounds of clay. She has 160 minutes available for making the cups and plates and has 20 pounds of clay on hand. If she makes a profit of $2 on each cup and $3 on each plate, how many cups and plates should she make to maximize her profit. Aurelia should make 7 cups and 0 plates to maximize her profit. Aurelia should make 0 cups and 8 plates to maximize her profit. Aurelia should make 2 cups and 7 plates to maximize her profit. Aurelia should make 7 cups and 2 plates to maximize her profit.

Accepted Solution

A:
let
 x: ceramic cups
 y: ceramic plates
 We have the following system of equations:
 10x + 20y = 160
 3x + 2y = 20
 We solve the system:
 Step 1:
 10x + 20y = 160
 -30x-20y = -200
 Step 2:
 -20x = -40
 x = -40 / -20 = 2
 Step 3:
 3x + 2y = 20
 2y = 20-3x
 y = (20-3x) / 2
 y = (20-3 * (2)) / 2 = 7
 Then, herr total benefit will be:
 2 * (2) + 3 * (7) = 25 $
 Answer:
 Aurelia should make 2 cups and 7 plates to maximize her profit