Answered

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 400 eggs and 750 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.)

Answer :

Answer:

In order to earn the largest profit, you should make 150 quarts of Creamy Vanilla and 100 quarts of Continental Mocha.

Step-by-step explanation:

You will make the largest profit when you use all your stock, and all of this is sold. We can find the number of each that are sold solving a system of equations.

I am going to say that:

x is the number of quarts of Creamy Vanilla

y is the number of quarts of Continental Mocha.

Each quart of Creamy Vanilla uses 2 eggs. Each quart of Continental Mocha uses 1 egg. There are 400 eggs in stock. So:

[tex]2x + y = 400[/tex]

Each quart of Creamy Vanilla uses 3 cups of cream. Each quart of Continental Mocha uses 3 cups of cream. There are 750 cups of cream in stock. So:

[tex]3x + 3y = 750[/tex]

Simplifying by 3

[tex]x + y = 250[/tex]

Solve the following system:

[tex]2x + y = 400[/tex]

[tex]x + y = 250[/tex]

From the second equation:

[tex]y = 250 - x[/tex]

Replacing in the first equation:

[tex]2x + y = 400[/tex]

[tex]2x + 250 - x = 400[/tex]

[tex]x = 150[/tex]

[tex]y = 250 - x = 250 - 150 = 100[/tex]

In order to earn the largest profit, you should make 150 quarts of Creamy Vanilla and 100 quarts of Continental Mocha.

Other Questions