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My coffee shop sells a multitude of selections of different types of coffee. The latte is the most popular of the choices and I'm wanting to maximize my profits from selling the vanilla and white chocolate lattes. There has been a demand for more lattes so I'm giving my customers what they have been wanting My shop also offers free wi-fi and makes the best coffee in town.

Restictions

I am only able to make up to 500 cups of each type of latte per month. Also, I cannot spend more than $1,000 per month on lattes.

Costs and Selling

A caramel latte costs me $2.00 to make, while a white chocolate latte costs me $1.50 to make. I can sell a caramel latte for $4.00 and a white chocolate latte for $3.00

Systems of Inequalities

C= Number of Caramel Lattes

W= Number of White Chocolate Lattes

C ≥ 0 C ≤ 500

W ≥ 0 W ≤ 500

4C+3W≤ 1000

Profits

I can find my profit by taking the money made and subtracting the money I have spent.

Cost= 2A + 1.5B

Sell= 4A + 3B

Profit= Cost - Sell

Profit= (4A + 3B) - (2A + 1.5B) OR Profit= 2A + 1.5B

Maximize Profits

(0,500) P= 2 (0) + 1.5 (500) = $750

(500,0) P= 2 (500) + 1.5 (0) = $1000

(125,500) P= 2 (125) + 1.5 (500) = $1000

(0,0) P= 2(0) + 1.5 (0) = $0

I will maximize my profits by making either 500 cups of caramel lattes a month and no white chocolate, or by making 125 caramel lattes and 500 white chocolate lattes a month. I believe that my customers would be most happy with me making 125 caramel lattes and 500 white chocolate lattes.

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