Revenue and Cost Functions

Question

A company that manufactures running shoes has a fixed cost of $300,000. Additionally, it costs $30 to produce each pair of shoes. They are sold at $80 a pair.

Write the cost function, C, of producing x pairs of running shoes.
Write the revenue function, R , from the sale of x pairs of running shoes.
Determine the break-even point. Describe what this means.

Answer 1

1. C = $30·x + $300,000
2. R = $80·x
3. Break even occurs when Cost = Revenue

        $30x + $300,000 = $80x

        Solve for x. 

 

Remember x is the number of shoes produced and sold, so the value of x is the number of shoes you need to produce and sell to break even