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# Cupcake Cookin'

### April 24th, 2014 hour 2

In my business, Cupcake Cookin', I will bake fresh cupcakes to be eaten by people looking for a fun little dessert. All cupcakes will be sold in singles with the only price difference being between the small and big cupcakes.

I won’t be able to produce more than 100 fresh large cupcakes per week and no more than 200 small cupcakes each week. In my startup phase I can’t spend more than \$800 each month. I have \$10,000 to spend and can’t use more than 75% on one product.

Business Plan: Costs & Selling Prices

The large cupcakes will cost \$4 a cupcake to produce and small cupcake will cost \$3 to produce. I can sell the large ones for \$7.50 a cupcake and \$6 for a small cupcake

Restrictions: Systems of Inequalities

x=# large cupcakes; y = # small cupcakes each week

x > 0, x < 100

y > 0, y < 200

4x + 3y < 800

4x < 7500

3y < 7500

My profits will be the money made at my selling price minus the costs.

x= # Large Cupcakes; y= # Small Cupcakes

Cost = \$4x + \$3y

Sell = \$7.50x + \$6y

Profit = sell – cost

P = (7.5x + 6y) – (4x + 3y) OR

P = 3.50x + 3y

Graphing it out

Maximize Profits

Profit = \$3.50x + \$3.00y

(0, 200) P = 3.5 (0) + 3(200) = \$600

(50, 200) P = 3.5(50) + 3(200) = \$775

(100, 133 1/3) P = 3.5 (100) + 3(133) = \$749

(100, 0) P = 3.5 (100) + 3(0) = \$350

I will maximize my profits each week if I produce 50 large cupecakes and 200 small cupcakes.