# Purple: Spring Clothing Line

In my business, Purple, I will design and make dresses as well as shoes. These dresses and shoes will be designed for the Spring but can be worn any season. I will sell the dresses individually as well as pairs of shoes individually.

I won't be able to produce more than 50 dresses a month and no more than 25 pairs of shoes each month. In my starting pup phase I can't spend more than \$900 each month. I have \$10,000 to spend and can't use more than 65% on one product.

# Business Plan: Costs & Selling Prices

Each dress with cost \$25 dollars to produce and each pair of shoes will cost \$30 dollars to produce.

I can sell the dresses for \$45 each and \$50 for each pair of shoes.

# Restrictions: Systems of Inequalities

x= # of dresses; y= # of pairs of shoes each month

x≥0, x≤50

y≥0, y≤25

25x+30y≤900

25x≤6500

30y≤6500

My profits will be the money made at my selling price minus the costs.

x= # of dresses; y= # of pair of shoes

Cost= \$25x+\$30x

Sell= \$45x+\$50y

Profit= sell - cost

P= (45x+50y) - (25x-30y) OR

P= 20x+20y

# Maximize Profits

Profit = \$20x + \$20y

(0,25) P = 20(0) + 20(25) = \$500

(6,25) P = 20(6) + 20(25) = \$620

(36,0) P = 20(36) + 20(0) = \$720

I will maximize my profits each month if I produce 36 dresses and 0 pairs of shoes.