# Linear Programming

### Alex Kretsinger 10/4/13

## Clothing Store

In my store, I'm selling long sleeve shirts and short sleeves shirts.

I have $10,000 to produce my clothing. I decided that I wouldn't order more than 9,000 of both short and long sleeve shirts and I wouldn't spend more than $10,000.

## Cost of Shirts

Short sleeve shirts come with 12 shirts in a box.

The cost per box is $20.

Each short sleeve shirt is $5.

Long sleeve shirts come with 8 shirts in a box.

The cost per box is $35.

Each long sleeve shirt is $10.

## Equations

Let x = Short Sleeve Shirts

Let y = Long Sleeve Shirts

### Inequalities representing constraints

• x ≥ 0

• y ≥ 0

• 12x + 20y ≤ 9,000

• 8x + 35y ≤ 10,000

### Equations Representing Profit

• p = s - c

• s = 60x + 80y

• c = 20x + 35y

• p = 40x + 45y

To maximize the profit I need to sell zero short sleeve shirts and 285 long sleeve shirts which adds up to $9,975.