A small company can produce up to 200 handmade sandals a month. The monthly cost, C, of producing x sandals is C(x) = 1000 + 5x. The monthly revenue, R, is given by R(x) = 75x - 0.4x2

Question

a. For what values of x is the revenue greater than the cost?
b. At what production levels will the company make a profit?
c. At what production levels will the company lose money?

Answer 1

(a) when R(x) > C(x) -- so just plug in their definitions and solve the inequality.
75x - 0.4x^2 > 1000+5x
16 < x < 159
(b) exactly the same question as (a)
(c) everywhere else than in (b)