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.
Business Plan: Restrictions
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
Business Plan: Profits
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
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.