Question 877125: Lily is currently selling ad space for $0.50 each post and she sells 100 spots a month. Once again, using her mathematical researching skills, she discovers that for every $0.02 increase in the price, she will lose 5 ad sales. At what price will Lilly be making the most money? At what price will she be making absolutely no money?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Lily is currently selling ad space for $0.50 each post and she sells 100 spots a month. Once again, using her mathematical researching skills, she discovers that for every $0.02 increase in the price, she will lose 5 ad sales. At what price will Lilly be making the most money? At what price will she be making absolutely no money?
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let x=number of $0.02 increases in the price
revenue=price*quantity
R=(.50+.02x)(100-5x)
R=50-.50x-.10x^2
R=-.10x^2-.50x+50
complete the square:
R=-.10(x^2+5x+6.25)+.625+50
R=-.10(x+2.5)^2+50.625
maximum revenue of $50.625 ocurs when x=-2.5
This is reducing the price=2.5*.02=.05 to $0.45 for each post
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For zero revenue:
0=-.10x^2-.50x+50
(x+25)(x-20)=0
x=-25 or x=20
which results increases in price of -$0.50 or $0.40
which results in selling prices of $0 and $0.90 which produces 0 revenue
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At what price will Lilly be making the most money? $0.45
At what price will she be making absolutely no money? $0.90
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