document.write( "Question 1208038: A candy store finds that it can make a profit of P dollars each month by selling x boxes of candy. Using the formula: P(x)=-.0013x^2+5.5x-800,how many boxes of candy must the store sell in order to maximize their profits?what is the maximum profit?
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Algebra.Com's Answer #846173 by ikleyn(52898) $\"\"$ $\"About$

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\n" ); document.write( "A candy store finds that it can make a profit of P dollars each month by selling x boxes of candy.
\n" ); document.write( "Using the formula: P(x)=-.0013x^2+5.5x-800, how many boxes of candy must the store sell
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document.write( "In this problem, the profit is a quadratic function representing a parabola.\r\n" );
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document.write( "Since the coefficient at x^2 is negative (it is -0.0013), the parabola is opened downward and has the maximum.\r\n" );
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document.write( "The maximum of any quadratic function y = ax^2 + bx + c with negative coefficient  \"a\"  is at\r\n" );
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document.write( "     = .\r\n" );
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document.write( "In our case it is   =  =  = 2115.384615.\r\n" );
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document.write( "Since the number of boxes is an integer number, we should round the number to 2115.\r\n" );
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document.write( "The maximum profit is then   =  = 5017.31 dollars (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved in full.\r
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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function see the lessons\r
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\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the vertex of a parabola\r
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\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher,
\n" ); document.write( "who is always with you to help.\r
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\n" ); document.write( "\n" ); document.write( "Learn the subject from there once and for all.\r
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