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# Business Plan

My business is a cupcakery. We are starting out with 2 types of cupcakes available for customers to buy individually. The first type is white cake with vanilla icing, and the second will be white cake with chocolate icing.

# Restrictions

I can only make 300 cupcakes with vanilla icing per month, and I can only make 400 of the cupcakes with chocolate icing per month. I can only spend \$500 per month. The chocolate iced cupcakes will sell for \$3, while the vanilla iced cupcakes will sell for \$2. It costs \$1 to make a cupcake with chocolate icing, and it costs \$0.75 to make a cupcake with vanilla icing.

# Systems of Inequalities

x=#of chocolate iced cupcakes

y=# of vanilla iced cupcakes

Profit Equation:

Sell

3x+2y=S

Cost

1x+0.75y=C

Profit

2x+1.25y=P

Restrictions:

x≤400

x≥0

y≤300

y≥0

1x+0.75y≤500

# Maximizing Profit

Profit:

2x+1.25y=P

Vertices of Feasible Region:

1. (0, 300) 2. (275, 300) 3. (400, 133) 4. (400, 0)

1. 2(0)+1.25(300)= \$375

2. 2(275)+1.25(300)=\$925

3. 2(400)+1.25(133)=\$966.25

4. 2(400)+1.25(0)= \$800

# Conclusion

To make the most profit, I should make and sell 400 chocolate iced cupcakes and 133 vanilla iced cupcakes.