Question

A small machine shop manufactures drill bits used in the petroleum industry. The shop manager estimates that the total daily cost (in dollars) of producing x bits is:   

                              C(x) = 1000+25x – 0.1x²

(a) Find Average cost (AC) and Marginal cost (MC) when Q=10.

(b) Further, if the selling price of a unit is 2x² + 9, find the Average Revenue (AR) and Marginal Revenue (MR).

(c) Calculate Average Profit (AP) and Marginal Profit (MR).                                                                     

Answer 1

C (x) = 1,000 + 25x - 0.1x^²

a) AC = TC / x

AC = (1,000 / x) + 25 - 0.1x

At x = 10, AC = (1,000 / 10) + 25 - 0.1 * 10 = 124

Marginal cost (First derivative of TC with respect to x) = 25 - 0.2x = 25 - 0.2 * 10 = 23

b) Selling price = 2x^² + 9

Total revenue = Selling price * x = 2x^³ + 9x

Average revenue = (TR / x) = 2x^² + 9

Marginal Revenue (First derivative of total revenue with respect to x) = 6x^² + 9

c) Profit = Total Revenue - Total Cost

Profit = 2x^² + 9 - 1,000 - 25x + 0.1x^²

Average Profit = (Profit / x) = 2.1x - 25 - (991 / x)

Marginal profit (First derivative of profit with respect to x) = 4.2x - 25