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
[tex]C(x)=100000+100x[/tex]
Selling price of 1 bike = $300
Selling price of x bikes = $300x
So, the revenue function is
[tex]R(x)=300x[/tex]
At break even, the profit is zero. It other words, cost and revenue are equal.
[tex]C(x)=R(x)[/tex]
[tex]100000+100x=300x[/tex]
[tex]100000=300x-100x[/tex]
[tex]100000=200x[/tex]
[tex]\dfrac{100000}{200}=x[/tex]
[tex]500=x[/tex]
Therefore, 500 bikes must be sold in order for the company to break even.
