document.write( "Question 84784: Susan is selling tickets to a concert. Seating capacity is 1,500 seats. The rate is $6.00. Susan knows that she can sell 1200 at this price. Every time that she increases the price by $0.75 then her sales decreases by half. write the equation. What is the maximum amount that she can make. \n" ); document.write( "

Algebra.Com's Answer #61079 by Edwin McCravy(20064) $\"\"$ $\"About$

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document.write( "Susan is selling tickets to a concert. Seating capacity is 1,500 seats. The\r\n" );
document.write( "rate is $6.00. Susan knows that she can sell 1200 at this price. Every time\r\n" );
document.write( "that she increases the price by $0.75 then her sales decreases by half. write\r\n" );
document.write( "the equation. What is the maximum amount that she can make.\r\n" );
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document.write( "Your teacher botched this problem.  First of all it is a calculus \"minimax\"\r\n" );
document.write( "problem, not an algebra problem, since it is not a quadratic.  Secondly Susan\r\n" );
document.write( "loses money if she increases the price even by $0.75, for only half the 1500\r\n" );
document.write( "seats, or 750, are then sold, and that only brings in $5062.50, whereas if\r\n" );
document.write( "she doesn't increase it at all, she takes in $9000.\r\n" );
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document.write( "If she increases    The price per      And the number      So her\r\n" );
document.write( " the price by       ticket is      of ticket sales is   intake is\r\n" );
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document.write( "      0              $6.00               1500            $9000.00\r\n" );
document.write( "    $0.75            $6.75                750            $5062.50\r\n" );
document.write( "    $1.50            $7.50                325            $2437.50\r\n" );
document.write( "    $2.25            $8.25                162            $1336.50\r\n" );
document.write( "    $3.00            $9.00                 81            $ 729.00\r\n" );
document.write( "    $3.75            $9.75                 40            $ 390.00\r\n" );
document.write( "    $4.50           $10.50                 20            $ 210.00\r\n" );
document.write( "    $5.25           $11.25                 10            $ 112.00\r\n" );
document.write( "    $6.00           $12.00                  5            $  60.00\r\n" );
document.write( "    $6.75           $12.75                  2            $  25.50\r\n" );
document.write( "    $7.50           $13.50                  1            $  13.50\r\n" );
document.write( "    $8.25           $14.25                  0            $   0.00\r\n" );
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document.write( "So she makes the most money by not increasing the price at all.\r\n" );
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document.write( "Tell your teacher he or she has botched this problem.\r\n" );
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document.write( "Here is an attempt at deriving the equation for it:\r\n" );
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document.write( "Let x = the number of $0.75 price increases\r\n" );
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document.write( "Then the price per ticket is $6.00 + $0.75x\r\n" );
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document.write( ">>..Every time that she increases the price by $0.75 then her sales \r\n" );
document.write( "decreases by half..<<\r\n" );
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document.write( "So x is also the number of times her sales get cut in half, so\r\n" );
document.write( "the 1500 is multiplied by  x times.\r\n" );
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document.write( "So the number of sales is 1500\r\n" );
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document.write( "So her total revenue R = (price per ticket)(number of tickets sold)\r\n" );
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document.write( "R = (6 + .75x)(1500\r\n" );
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document.write( "So you see it is an exponential equation, not a quadratic, which\r\n" );
document.write( "is probably what your teacher intended it to be.\r\n" );
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document.write( "Edwin

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