Consider a product whose selling price depends on the quantity sold through the…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Consider a product whose selling price depends on the quantity sold through the linear relation p=a−bx, where a,b>0 and x denotes the number of units sold.
Answer the following questions about the resulting revenue, cost and profit functions.
(i) Explain why the total revenue function R(x) is a quadratic polynomial in x and describe its general opening direction.
(ii) Describe, without performing any calculation, how you would locate the quantity that maximises the profit when a differentiable cost function C(x) is also given.
(iii) State, with reason, an additional mathematical condition that must be checked after the stationary point is obtained to ensure that the profit is actually maximised at that quantity.