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