g 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 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

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 equationI 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 = 750Now we have to solve the following system of equations1) 2x + y = 4502) 3x + 3y = 750The first thing i am going to do is simplify the equation 2) by 32) 3(x+y)/3 = 750/32) x+y = 250So now, we have the following system1) 2x + y = 4502) x + y = 250I am going to write y as a function of x in 2), and replace in 1)y = 250 - xReplacing in 1)2x + 250 - x = 4502x - x = 450 - 250x = 200You should make 200 quarts of Creamy VanillaFrom 2), we havey = 250 - x = 250 - 200 = 50You should make 50 quarts of Continental Mocha