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 = 2610 30x where p is the price per unit in dollars when x thousand television sets are sold.

(a) Find the revenue function. Note that R(x) will be in terms of thousands of dollars.

R(x) =  

(b) Determine the number of sets that must be sold in order to maximize the revenue.
_______ sets

(c) To the nearest whole dollar, what is the maximum revenue? Note that R(x) is in terms of thousands of dollars.

$:

(d) To the nearest cent, what is the price per unit when the revenue is maximized?
$______ per unit

Solution

a) R(x) = x*P(x) = x( 2610 -30x) = 2610x -30x^2

b) To maximise revenue: find dR/dx =0

2610 - 6x =0

x = 435 thousand sets

c) Maximum Revenue occurs at x =435

R(x) = 2610x -30x^2 at x = 435

= $ 946125

d) price per unit when the revenue is maximized = $ 946125/435*1000 = $2.17 per unit