document.write( "Question 1181585: When tickets at a dance cost $4, the expected attendance is 300 people. for every $0.10 increase in ticket price, the dance committee projects that the attendance will decrease by 5 people. what would be the maximum revenue? what ticket price would maximize the revenue? \n" ); document.write( "

Algebra.Com's Answer #811493 by Edwin McCravy(20054) $\"\"$ $\"About$

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document.write( "Ticket price as is = $4\r\n" );
document.write( "Attendence with ticket price as is = 300\r\n" );
document.write( "Revenue with ticket price as is = (300)($4) = $1200\r\n" );
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document.write( "Let x = the number of ten-cent increases made in the ticket price.\r\n" );
document.write( "Then the ticket price will increase by $0.10x, making the \r\n" );
document.write( "new higher ticket price be $4+$0.10x.\r\n" );
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document.write( "That will also cause the attendance to decrease by 5x.\r\n" );
document.write( "Then the new lower attendance will be 300-5x.\r\n" );
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document.write( "Let y = the new higher (hopefully) revenue (the amount of money taken in\r\n" );
document.write( "from selling all the tickets at the new higher ticket price and the new\r\n" );
document.write( "lower attendance).\r\n" );
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document.write( "Using FOIL on the right side,\r\n" );
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document.write( "The maximum new attendance y will occur at the vertex of the parabola,\r\n" );
document.write( "since the parabola opens downward (since the leading coefficient, a, is\r\n" );
document.write( "negative).  We use the vertex formula\r\n" );
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document.write( "So we should make 10 ten-cent increases in the ticket price,\r\n" );
document.write( "which makes the new higher ticket price $5 and the new lower attendance\r\n" );
document.write( "50 fewer or only 250. So the new higher revenue will be (250)($5) or $1250.\r\n" );
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document.write( "We could also have substituted 10 for x in\r\n" );
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document.write( "and gotten the same answer $1250.\r\n" );
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document.write( "Edwin

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