A firm is developing a new product. An early introduction (beating rivals to mar

Question

A firm is developing a new product. An early introduction (beating rivals to market) would greatly enhance the company’s revenues. However, the intensive development effort needed to expedite the introduction can be very expensive. Revenues and costs associated with the new product are given by:
R = 720 – 12t and C = 600 – 20t + 0.2t2
where t is the introduction date (in months from now). Some executives have argued for an expedite introduction date, 15 months from now (t = 15). Do you agree? If not, what introduction date would you recommend?

Explanation / Answer

I do not agree.

Profit function , P = R - C = ( 720 – 12t ) - ( 600 – 20t + 0.2t2) = 120 + 8t - 0.2t2)

To find the maxime, find the first order derivative, dP/dt = -0.4t + 8 = 0,   

=>     t = 20 months

So I will recommend the introduction date 20 months from now, which will maximise the profit. .

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