document.write( "Question 1169652: A promoter of a show realizes that , if the price per ticket is set at 650.00 , only 50 people will watch the show . He also estimates that for every 50.00 decrease in the price of the ticket , the number of people watching the show will increase by 10. What should be the price per ticket so that the revenue ( number of tickets sold x price per ticket ) is a maximum ? What is the maximum value ?\r
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Algebra.Com's Answer #794524 by ankor@dixie-net.com(22740)\"\" \"About 
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if the price per ticket is set at 650.00 , only 50 people will watch the show .
\n" ); document.write( " He also estimates that for every 50.00 decrease in the price of the ticket, the number of people watching the show will increase by 10.
\n" ); document.write( " What should be the price per ticket so that the revenue (number of tickets sold x price per ticket) is a maximum ?
\n" ); document.write( "What is the maximum value?
\n" ); document.write( "Revenue = price * no. of tickets sold
\n" ); document.write( "R(x) = (650-50x)*(50+10x)
\n" ); document.write( "FOIL
\n" ); document.write( "R(x) = 32500 + 6500x - 2500x - 500x^2
\n" ); document.write( "arrange as a quadratic function
\n" ); document.write( "R(x) = -500x^2 + 4000x + 32500
\n" ); document.write( "Simplify, divide by -500
\n" ); document.write( "y = x^2 - 8x - 65
\n" ); document.write( "Find the the axis of symmetry
\n" ); document.write( "x = 8/(2*1)
\n" ); document.write( "x = 4
\n" ); document.write( "therefore
\n" ); document.write( "(10(4)+50) = 90 ticket sold for max revenue
\n" ); document.write( "and
\n" ); document.write( "(650-(4*50)) = $450 is the price of the tickets then
\n" ); document.write( "and
\n" ); document.write( "90 * 450 = $40500 is max revenue
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