# Austin Stark - 10/2/14 -

Drum Stick Business

# Drum Stick Business

My business manufactures two types of drum sticks. Black Wood drum sticks and White Wood drum sticks. In the following equations, x = Number of White Wood, and y = Number of Black Wood. The cost to manufacture compared to my budget of $10,000 can be shown as 5x+7y=10,000.

In this business I sell white sticks for $8.50 and black sticks for $11. So the money made from the sales can be shown as 8.5x+11y. But to calculate profit, I need to factor out the manufacturing cost, so my profit=3.5x+4y

The restrictions of the business say that my products have to be equal to or above 0 however, because spending money for the loss of a product makes no sense for a business. I can show this with x>=0 and y>=0. It also says I cannot spend more than 3/4 of my budget on one product, shown by 5x<=7,500 and 7y<=7,500.

# Linear Programming

Here we see the linear program created through graphing these equations. I can use the vertices from the graph as the variables in my profit equation, 3.5x+4y, to find how much of each product I should buy to maximize my profit. So after plugging in (0, 1071), (500, 1071), (1500, 357), and (1500, 0), I found that making 1500 paris of white sticks, and 357 pairs of black sticks, will allow me to maximize my profit. So 3.5(1500) + 4(357) = Maximum Profit of $6628.