A cosmetics company is planning the introduction and promotion of a new lipstick

Question

A cosmetics company is planning the introduction and promotion of a new lipstick line. The marketing research department has found that the demand in a particular city is given approximately by

A cosmetics company is planning the introduction and promotion of a new lipstick line. The marketing research department has found that the demand in a particular city is given approximately by where x thousand lipsticks were sold per week at a price of p dollars each. At what price will the weekly revenue be maximized?

Explanation / Answer

Price per lipstick = 11e^-x

Number of lipsticks = x (in thousands)

Revenue = x*11e^-x

To maximise, R'(x) = 0

11( e^-x - x*e^-x) = 0

e^-x * (1 - x) = 0

Thus, x = 1

p = 11/e = 4.047 dollars

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