# Hangin' Up n' Out

### Linear Programming Project: Cailean Williams

Ever find yourself in need of hanging something, but you have no rope or stool to hang it with? Boy have we got the store for you! After years of frustration at never being able to hang anything, I have decided to help the fellow man. Here at Hangin' Up n' Out™ we have stools and ropes for all of your hanging needs!

## Cost Models

I am willing to spend up to \$3,000 a month on product

Each bundle of rope (x) costs \$3 to produce

Each stool (y) costs \$13 to produce

3x + 13y ≤ 3000

## Profit Models

I will be selling the bundles of rope (x) at \$5 per bundle. They are easy to produce and store so very little mark-up

I will sell each stool (y) at \$20 per stool. There is a lot of effort put into hand-crafting each and every stool, and we take pride in our woodworking

(5x + 20y) - (3x + 13y) = P

## Restrictions

I can make up to 500 bundles per month because they are easy to produce and easy to store

I can only make up to 200 stools per month because we will be hand crafting each and every stool for sale

x ≤ 500

y ≤ 200

## Maximum Profit

Using my profit equation of (5x + 20y) - (3x + 13y) = P I can determine the best number of products to make

(5(133) + 20(200)) - (3(133) + 13(200)) = \$1666

(5(500) + 20(115)) - (3(500) + 13(115)) = \$805

Therefore my maximum profit is achieved when I produce 133 bundles of rope and 200 stools