MATH SOLVE

3 months ago

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

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