# Hit The Pavement: A Running Store

### A fine selection of running wear

Kyle Gabrielson

College Algebra

Hour 6

With running becoming an increasingly popular sport, it was only fitting to open a running store. Selling a variety of of running items. Ranging from shoes, and shorts, to sport watches and gels. Come in and check us out to meet our knowledgeable staff, and you can leave in the best shoes you've ever owned.

### Restrictions:

I am only able to buy up to 500 pairs of shoes  per month. Also, I cannot spend more than \$3,000 per month on shoe purchases.

### Costs and Selling:

A pair of Nikes costs \$30.00 to buy, while a pair of Vibram Five Fingers cost \$40.00 to buy. I can sell a pair of Nikes for \$100.00 and a pair of Vibrams for \$120.00

### Systems of Inequalities:

N= Number of Nikes (x)

V= Number of Vibrams (y)

N ≥ 0 N ≤ 500

V≥ 0 V ≤ 500

100N+120V≤ 3,000

### Profits:

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

Cost= 30A + 40B

Sell= 100A + 120B

Profit Equation: 70A+80B=Profit

Profit= Cost - Sell

Profit= (100A + 120B) - (30A + 40B)

### Maximize Profits:

(0,25) P= 30 (0) + 40 (25) = \$1,000

(0,0) P= 30 (0) + 40 (0) = \$0

(30,0) P= 30 (30) + 40 (0) = \$900