document.write( "Question 877332: A theater has 550 seats. The theater will sell tickets for all seats if the tickets cost $30 each. However, for each $4 increase in ticket price, 20 fewer tickets are sold. What ticket price will generate the most revenue and what is the maximum revenue? \n" ); document.write( "
Algebra.Com's Answer #529320 by lwsshak3(11628)\"\" \"About 
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A theater has 550 seats. The theater will sell tickets for all seats if the tickets cost $30 each. However, for each $4 increase in ticket price, 20 fewer tickets are sold. What ticket price will generate the most revenue and what is the maximum revenue?
\n" ); document.write( "***
\n" ); document.write( "let x=number of $4 increase in ticket prices
\n" ); document.write( "Revenue=price*number of tickets sold.
\n" ); document.write( "R=(30+4x)*(550-20x)
\n" ); document.write( "R=16500+1600x-80x^2
\n" ); document.write( "R=-80x^2+1600x+16500
\n" ); document.write( "complete the square:
\n" ); document.write( "R=-80(x^2-20x+100)+8000+16500
\n" ); document.write( "R=-80(x-10)+24500
\n" ); document.write( "x=10
\n" ); document.write( "number of $4 increase in ticket prices=10
\n" ); document.write( "maximum revenue will be generated when ticket price is increased by $40 to $70
\n" ); document.write( "maximum revenue =$24,500 \n" ); document.write( "
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