Gyou 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 450 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

You should make 200 quarts of Creamy Vanilla and 50 quarts of Continental Mocha to earn the largest profit.

Step-by-step explanation:

You are going to earn the largest profit when you manage to use all the eggs and cups of cream that you have in stock.

This problem can be solved by a first order equation

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 450 eggs in stock, so:

2x + y = 450.

The problem also states that each quart of Creamy Vanilla uses 3 cups of cream and that each quart of Continental Mocha uses 3 cups of cream. There are 750 cups of cream in stock, so:

3x + 3y = 750

Now we have to solve the following system of equations

1) 2x + y = 450

2) 3x + 3y = 750

The first thing i am going to do is simplify the equation 2) by 3

2) 3(x+y)/3 = 750/3

2) x+y = 250

So now, we have the following system

1) 2x + y = 450

2) x + y = 250

I am going to write y as a function of x in 2), and replace in 1)

y = 250 - x

Replacing in 1)

2x + 250 - x = 450

2x - x = 450 - 250

x = 200

You should make 200 quarts of Creamy Vanilla

From 2), we have

y = 250 - x = 250 - 200 = 50

You should make 50 quarts of Continental Mocha