Question

The revenue function for a small t-shirt company is r(x)=18x. The cost function is c(x)=8x+960. Find the number of t-shirts that have to be sold to break-even.

Answer 1

Profit is revenue minus cost. This means there is a function, P(x), that is profit.

P(x) = R(x) - C(x)

Breaking even is the point where revenue starts to overtake cost. It is therefore the point where P(x) = 0. Since these are all linear functions, you know that after that point the business is profitable.

P(x) = 0
R(x) - C(x) = 0
13000x - (9000x+48000) = 0
13000x - 9000x - 48000 = 0
4000x - 48000 = 0
4000x = 48000
x = 48000/4000
x = 12

At 12 units the business breaks even.