Question

Suppose a company has a revenue stream that can be modeled by R(t)=?0.045t^2+0.72t+0.176 in millions of dollars, further suppose that costs and expenses can be modeled by C(t)=?0.012t^2+0.12t+0.091, where t is the number of years past 1985.

The year in which the maximum profit occurs is __________  (If needed, round to the nearest tenth of a year.)

Answer 1

Maximum profit occurs when marginal revenue is equal to marginal cost

So after differenciation of revenue and cost functions we get

Marginal revenue(MR(t)) =0.045*2*t + 0.72 = 0.09t + 0.72

Mariginal cost (MC(t)) = 0.012*2*t + 0.12 = 0.024t + 0.12

So, we have 0.09t + 0.72 = 0.024t + 0.12

                   0.066 t = -0.6

                        t = 9.09 years