Given the function, C(X), and the revenue function, R(x), find the number of x units that must be sold to break even.

Question

C(x)=9000x+48000

R(x)=13000x

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.