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

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
RELATED QUESTIONS
Calculators are sold to students for 1000 dollars each. Five hundred students are willing (answered by stanbon)

Hans paid $1.50 ea. For programs to the game. He sold all but 20 of them for $ 3.00 ea.... (answered by jim_thompson5910)

Tickets are available at 3 prices for a series of concerts. On a certain evening n people (answered by josmiceli)

Hans paid $1.50 each for programs to the game. He sold all but 20 of them for $3 each and (answered by ankor@dixie-net.com)

Hann paid $1.50 each for programs to the game, he sold all but 20 of them for $3 dollars... (answered by ankor@dixie-net.com)

I am unsure of how to work this problem out ??? Three software applications are priced as (answered by solver91311)

Please help! If you can show me what I did wrong, that would be helpful, thanks 1.... (answered by solver91311)

Hans paid $1.50 each for programs to the game. He sold all but 20 of them for $3.00 each... (answered by checkley71,BGluvsmath)

Martin sold his computer and software for $900, receiving three times as much for the... (answered by ewatrrr)