The demand function for a particular brand of LCD TV is give

The demand function for a particular brand of LCD TV is given by p = 2135 35x where p is the price per unit in dollars when x thousand television sets are sold.

Solution

The demand function for a particular brand of LCD TV is Given by p=2800-35x where p is the price per unit in dollars when x thousand television sets are sold.

Determine the number of sets that must be sold in order to maximize the revenue.

To the nearest whole dollar, what is the maximum revenue?

To the nearest cent, what is th price per unit when the revenue is maximized?

Solution :

Revenue R(x) = x*p(x) = x(2800 -35x)

a) To amximise revenue find dR/dx = 2800 - 70x =0

x = 2800/70 = 40 sets of LCD

b) Maximum Revenue plug x= 40 in R(x)

R(40) = 40 ( 2800 -35*40) = $ 56000

c) Price per unit = Total revenue/ Total LCD sold = $ 1400