Question

Craig Browning bakes cookies for the elementary school cookie sale. his chocolate cookies sell for $1.00 a dozen, and his oatmeal brownie cookies sell for $1.50 a dozen. he will bake up to 20 dozen chocolate chip cookies, and up to 40 oatmeal brownie cookies, but no more than 50 dozen cookies total. also, the number of oatmeal cookies will be no more than three times the number of chocolate chip cookies. how many of each kind should craig make in order for the elementary school to make the most money? how much money will this be?

Answer 1

Let, the number of chocolate cookies be x dozens

Let, the number of oatmeal brownie cookies be y dozens

Maximum number of chocolate chip cookies that can be baked is 20 implies

Maximum number of oatmeal brownie cookies that can be baked is 40 implies

Maximum total number of cookies is 50 implies

No of oatmeal cookies are no more than 3 times the number of chocolate chip cookies implies

Plot the above inequalities on the graph and find the feasible reion

The feasible region is shown above. The profit function is

The optimal solution to the profit function occurs at the corner points of the feasible region. Find the profit at the four corner points

Hence, the maximum profit occurs at (12.5,37.5) which implies 12.5 dozen chocolate chip cookies and 37.5 dozen oatmeal cookies should be ordered. Maximum profit at the above level of production is $68.75