# Brooke's CakesCustom Cakes designed by Brooke

### Brooke LoudonApril 24, 2015Linear Programming Project

Brooke's Cakes is a bakery shop that designs custom cakes AND tasty cupcakes. Prices are reasonable, and there are many flavors offered. Cake sizes range from small to extra large for whatever occasion, and cupcakes are a standard size cupcake.

The cakes will cost \$5 to make and the cupcakes will cost \$2 to make.

I will be selling the cakes for \$25 and the cupcakes for \$5, making a profit of \$20 and \$3 respectively.

x=# of cakes                        y=# of cupcakes

Cost= 5x + 2y

Sell= 25x + 5y

Profit= Sell - Cost

P= (25x + 5y) - (5x + 2y)

or

p= 20x + 3y

Restrictions: I won't be able to produce more than 1,500 cupcakes a month and 250 cakes a month. I will limit myself to \$800 a month, and I have \$10,000 to spend. I won't spend more than 75% on a single product.

x= # of cakes

y= # of cupcakes

x ≥ 0,  x ≤ 250

y ≥ 0,  y ≤ 1,500

5x + 2y ≤ 800

5x ≤ 7500

2y ≤ 7500

Maximize Profits:

(0, 400) P= 20(0) + 3(400) = 1,200

(160, 0) P= 20(160) + 3(0) = 3,200

I will maximize my profits each month if I make 160 cakes and don't focus my company on cupcakes, making my business just a cake bakery. This will make me \$3,200 a month.