Math, microeconomics

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 500 eggs and 900 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? (If an answer does not exist, enter DNE.)

Creamy Vanilla ......... quarts

Continental Mocha ....... quarts

Answer 1

E +3C = V

2E+3C =M

3V+2M = P

E=500

C =900

Vanilla requires less ingredients (1E<2E) and has more profit ($3>$2)

so put all ingredients into Vanilla, 0 quarts into Mocha

300E + 3(300)C = 300 quarts of Vanilla

300V at $3 per V = $900 max Profit with 200 Eggs left over

put all into Mocha, then

2(250)+3(250) =250 quarts of Mocha

P= 2(250) =$500 with 150 Cream left over

the more you put into Mocha, the less you put into Vanilla and the less the Profit

$900>$500