document.write( "Question 965267: Must develop a quadratic function in order to solve the problem: A store sells 6000 gallons of paint each week for $15 per gallon. For each $1 decrease in the price, the store will sell an additional 1000 gallons each week. What should the sale price be to maximize the income?\r
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Algebra.Com's Answer #590003 by Edwin McCravy(20055) $\"\"$ $\"About$

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Must develop a quadratic function in order to solve the problem: A store sells
\n" ); document.write( "6000 gallons of paint each week for $15 per gallon. For each $1 decrease in the
\n" ); document.write( "price, the store will sell an additional 1000 gallons each week. What should the
\n" ); document.write( "sale price be to maximize the income?\r
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document.write( "Let x = the number of dollar decreases.\r\n" );
document.write( "Let y = the income with x dollars degreases.\r\n" );
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document.write( "For each $1 decrease in the price, the store will sell an additional 1000 gallons each week. \r\n" );
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document.write( "Number of gallons sold after x dollar decreases = 6000 + 1000x\r\n" );
document.write( "Price per gallon after x dollar decreases = $15-$x\r\n" );
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document.write( "Income = y = (6000+1000x)(15-x)\r\n" );
document.write( "         y = 90000-6000x+15000x-1000x^2\r\n" );
document.write( "         y = 90000+9000x-1000x^2\r\n" );
document.write( "         y = -1000x^2+9000x+90000\r\n" );
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document.write( "Compare to\r\n" );
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document.write( "         y = ax^2+bx+c\r\n" );
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document.write( "a= -1000, b = 9000\r\n" );
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document.write( "Use vertex formula:\r\n" );
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document.write( "x-coordinate of vertex = -b/(2a) = -(9000)/(2*-1000) = -9000/(-2000) = 4.5\r\n" );
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document.write( "Therefore decreasing the price 4.5 dollar decreases, which means a reduction\r\n" );
document.write( "of $4.50 will yield the maximum income.\r\n" );
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document.write( "So the sale price should be $15-$4.50 = $10.50 per gallon, to maximixe\r\n" );
document.write( "income.\r\n" );
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document.write( "Edwin

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