The demand function for a particular brand of LCD TV is given by p = 2610 30 x w
ID: 3408472 • Letter: T
Question
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
Explanation / Answer
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
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