Answer:
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
