SOLUTION: Computer software programs are sold for $20 each. Three hundred people are willing to buy them at this price. For every $5 increase in price, there are 30 fewer people willing to b
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Question 1160819: Computer software programs are sold for $20 each. Three hundred people are willing to buy them at this price. For every $5 increase in price, there are 30 fewer people willing to buy the software. Calculate the selling price that will produce the maximum revenue. What maximum revenue? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Computer software programs are sold for $20 each.
Three hundred people are willing to buy them at this price.
For every $5 increase in price, there are 30 fewer people willing to buy the software.
Calculate the selling price that will produce the maximum revenue.
:
let x = no. of 30 people groups subtracted
and
let x = no. $5 increases in price
:
Rev = price * units sold
R(x) = (20+5x)(300-30x)
FOIL
R(x) = 6000 - 600x + 1500x - 150x^2
A quadratic equation
y = -150x^2 + 900x + 6000
Max occurs on the axis of symmetry, x - -b/(2a)
x =
x = +3 for max revenue
therefore
a 3(5) = $15 increase in price,
20 + 15 = $35 is the price for max revenue
however
you lose 3(30) = 90 customers, 300 - 90 = 210 customers
:
"What is the maximum revenue?"
$35 * 210 = $7350
