document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #529228 by lwsshak3(11628)\"\" \"About 
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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?
\n" ); document.write( "***
\n" ); document.write( "let x=number of $0.02 increases in the price
\n" ); document.write( "revenue=price*quantity
\n" ); document.write( "R=(.50+.02x)(100-5x)
\n" ); document.write( "R=50-.50x-.10x^2
\n" ); document.write( "R=-.10x^2-.50x+50
\n" ); document.write( "complete the square:
\n" ); document.write( "R=-.10(x^2+5x+6.25)+.625+50
\n" ); document.write( "R=-.10(x+2.5)^2+50.625
\n" ); document.write( "maximum revenue of $50.625 ocurs when x=-2.5
\n" ); document.write( "This is reducing the price=2.5*.02=.05 to $0.45 for each post
\n" ); document.write( "..
\n" ); document.write( "For zero revenue:
\n" ); document.write( "0=-.10x^2-.50x+50
\n" ); document.write( "(x+25)(x-20)=0
\n" ); document.write( "x=-25 or x=20
\n" ); document.write( "which results increases in price of -$0.50 or $0.40
\n" ); document.write( "which results in selling prices of $0 and $0.90 which produces 0 revenue
\n" ); document.write( "..
\n" ); document.write( "At what price will Lilly be making the most money? $0.45
\n" ); document.write( "At what price will she be making absolutely no money? $0.90 \n" ); document.write( "
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