A firm’s revenue (in thousand rupees) from selling hundred units of a product is…

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A firm’s revenue (in thousand rupees) from selling

x

hundred units of a product is modelled by

R(x)=(x^{2}+2x+1)(50-2x), \; 0\le x\le25.

(a) Obtain the marginal revenue function

R'(x)

. (b) Determine the value of

x

that maximises the revenue. (c) Calculate the maximum possible revenue (in thousand rupees) the firm can earn. (d) Verify that the value of

x

found in part (b) indeed gives a maximum by examining the nature of

R'(x)

on either side of the point.