Question

You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 350 eggs and 600 cups of cream. You make a profit of $3 on each quart of Creamy Vanilla and $2 on each quart of Continental Mocha. How many quarts of each flavor should you make to earn the largest profit? HINT (See Example 2.] (If an answer does not exist, enter DNE.) Creamy Vanilla quarts Continental Mocha quarts

Answer 1

Answer:

You should make 150 quarts of Creamy Vanilla and 50 quarts of Continental Mocha.

Step-by-step explanation:

This problem can be solved by a system of equations.

The largest profit is going to earned when all the eggs and cups of cream in stock are used.

I am going to call x the number of quarts of Creamy Vanilla and y the number of quarts of Continental Mocha.

The problem states that each quart of Creamy Vanilla uses 2 eggs and each quart of Continental Mocha uses 1 egg. There are 350 eggs in stock, so:

$2x + y = 350$

Each quart of Creamy Vanilla uses 3 cups of cream, as does each quart of Continental Mocha. There are 600 cups of cream in stock.

So:

$3x + 3y = 600$ Simplifying by 3.

$x + y = 200$

We have the following system

$1)2x + y = 350$

$2)x + y = 200$

I am going to multiply 2) by (-1) and then add with 1), so i can eliminate y

$1)2x + y = 350$

$2)-x - y = -200$

$2x - x + y - y = 350 - 200$

$x = 150$

$x + y = 200$

$y = 200 - 150 = 50$

You should make 150 quarts of Creamy Vanilla and 50 quarts of Continental Mocha.