Given the cost function, c(x), and the revenue function, r(x), find the number of units x that must be sold to break even c(x)=9000x+72000 r(x)=15000x

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) = 0R(x) - C(x) = 015000x - (9000x+72000) = 015000x - 9000x - 72000 = 06000x - 72000 = 06000x = 72000x = 72000/6000x = 12 At 12 units the business breaks even.