SOLUTION: A manufacture charges $24 for stereo headphones and has been selling about 1000 of them a week. He estimates that for every $1 price reduction, 100 more headphones can be sold per
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Question 272692: A manufacture charges $24 for stereo headphones and has been selling about 1000 of them a week. He estimates that for every $1 price reduction, 100 more headphones can be sold per week. What price will maximize the total revenue? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A manufacture charges $24 for stereo headphones and has been selling about 1000 of them a week.
He estimates that for every $1 price reduction, 100 more headphones can be sold per week.
What price will maximize the total revenue?
;
Let x = no. of $1 price reductions and no. of 100 more headphones sold
;
R(x) = (24 - x)(1000 + 100x)
FOIL
R(x) = 24000 + 2400x - 1000x - 100x^2
:
R(x) = 24000 + 1400x - 100x^2
in standard form
-100x^2 + 1400x + 24000 = 0
:
A quadratic equation; find the axis symmetry which will be the value for x that
gives max revenue; x = -b/(2a); In this equation; a= -100, b = 1400
x =
x = +7: no of dollar decreases for max revenue
;
24 - 7 = $17 for max revenue
:
Find max revenue, substitute 7 for x in the original equation
R = -100(7^2) + 1400(7) + 24000
R = -4900 + 9800 + 24000
R = $28,900
:
:
Check: 1700 items * $17 = 28900
