Shoe Company

Question

A shoe company produces batches of leather shoes and boots. Each batch is made from a starting material of 2000 square feet of leather. A pair of boots requires 10 square feet of leather to produce, and a pair of shoes requires 3 square feet. A consultant is brought in to assess the production process, and he suggests an adjustment based on market analysis. The demand for boots is on the rise, and a single pair can now be sold for $300, whereas a pair of shoes sells for $75. Assuming all other production costs are the same, how many pairs of boots should be produced in order to maximize profits?

Answer 1

200 boots.

 

Since the goal is to maximize profits, the product with the highest price should be produced in the largest quantity unless there is a constraint on production.

 

Boots fetch a price of $300 per pair or 30 (300/10) per square foot. Whereas shoes fetch a price of $75 per pair or $25 per square foot.

 

Hence to maximize profits the entire 2000 square feet of raw material should be used to produce boots. The maximim profit will be 200 boots @ $300 each = $60,000