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.
Question
Answer:
letx: 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
solved
general
10 months ago
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