Question

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

Answer 1

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.