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# ~Cakes Galore~Red Velvet & Banana Cupcakes

### Amy Taylor6th Hour - Due: 5/2/14

In the business I'm creating, I will be selling cupcakes. My main cupcakes are red velvet and banana.

I cannot produce more than 150 red velvet cupcakes per month & I cannot produce more than 200 banana cupcakes per month. In my starting month, I cannot spend more than \$1,000.

**Costs & Selling Prices:

The red velvet cupcakes will cost \$5 and the banana cupcakes will cost \$3 to produce. I will sell the red velvet cupcakes for \$9 and the banana cupcakes for \$5.

**Systems of Inequalities:

x=# of red velvet cupcakes, y=# of banana cupcakes

x≥0, x≤150

y≥0, y≤200

5x+3y≤1,000

My profits will be the \$ made by my selling prices minus the costs to produce.

x=# of red velvet cupcakes, y=# of banana cupcakes

Cost= \$5x + \$3y

Sell= \$9x + \$5y

Profit = Sell-Cost

P= (9x+5y) - (5x+3y) =

P=4x+2y

**Maximize Profits:

Points from grapher: (0,200), (80,200), (150,90), & (150,0)

(o,200) P= 4(0) + 2(200) = \$400

(80,200) P= 4(80) + 2(200) = \$720

(150,90) P= 4(150) + 2(90) = \$780********

(150,0) P= 4(150) + 2(0) = \$600

**Conclusion:

I will maximize my profits each month if I produce 150 red velvet cupcakes & 90 banana cupcakes.