Question

Edals of Petals, a bike manufacturer that makes flower-themed bikes, has a fixed cost of $100,000 due to the equipment necessary to make the bicycles. Additionally, each bike costs $100 in labor and materials to make. If each bike sells for $300, how many bikes must be sold in order for the company to break even?

Answer 1

Given:

Fixed cost = $100,000

Additional cost = $100 on each bike

Selling price = $300 each bike

To find:

The number of bikes that must be sold in order for the company to break even.

Solution:

Let x be the number of bikes.

Additional cost of 1 bike = $100

Additional cost of x bikes = $100x

So, the cost function is

Total cost = Fixed cost + Additional cost

`C(x)=100000+100x`

Selling price of 1 bike = $300

Selling price of x bikes = $300x

So, the revenue function is

`R(x)=300x`

At break even, the profit is zero. It other words, cost and revenue are equal.

`C(x)=R(x)`

`100000+100x=300x`

`100000=300x-100x`

`100000=200x`

`(100000)/(200)=x`

`500=x`

Therefore, 500 bikes must be sold in order for the company to break even.