Question

The demand for a certain product is represented by the equation p = 500 + 25x - `(x^2)/(3)` in rupees, where x is the number of units and p is the price per unit.  Find:
(i) Marginal revenue function.
(ii) The marginal revenue when 10 units are sold.

Answer 1

The demand function for a certain product is represented as:

p = 500 + 25x - `(x^2)/(3)` , p being price per unit

If R be the total revenue for x units, then
R = p. x = 500x + 25x² - `(x^3)/(3)` 

The Marginal Revenue (MR) is given as:
MR = `(d(R))/(dx)` = 500 + 50x - x²

Marginal Revenue when 10 units are sold i.e., put x = 10
(MR)₁₀ = 500 + 50(10) – (10)² = 500 + 500 – 100 = 900.