document.write( "Question 1192479: The cost function for a container company is c(x)=10x+30 and the revenue function is r(x)=-x^2+24x where x is the number of containers sold in thousand. Determine the profit function for the number of containers sold. Then determine the number of containers sold that maximizes profit\r
\n" ); document.write( "\n" ); document.write( "I got P(x)=-x^2-8x-30 and the x would be -4 but that negative confuses me how do you sell -4 000 contains? \n" ); document.write( "
Algebra.Com's Answer #824346 by ikleyn(52777)\"\" \"About 
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\n" ); document.write( "The cost function for a container company is c(x)=10x+30 and the revenue function is r(x)=-x^2+24x
\n" ); document.write( "where x is the number of containers sold in thousand.
\n" ); document.write( "(a) Determine the profit function for the number of containers sold.
\n" ); document.write( "(a) Then determine the number of containers sold that maximizes profit
\n" ); document.write( "I got P(x)=-x^2-8x-30 and the x would be -4 but that negative confuses me how do you sell -4 000 contains?
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\n" ); document.write( "\n" ); document.write( "            The formula for the profit function  P(x) = -x^2 - 8x - 30,  which you  \" got \" \r
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document.write( "The correct formula for the profit is\r\n" );
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document.write( "    P = Revenue - Cost,\r\n" );
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document.write( "or\r\n" );
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document.write( "    P(x) = (-x^2 + 24x) - (10x + 30) = -x^2 + 14x - 30.\r\n" );
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document.write( "It is the  ANSWER  to question (a).\r\n" );
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document.write( "To get the number of containers that maximizes the profit, use the formula\r\n" );
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document.write( "    \"x%5Bmax%5D\" = \"-b%2F%282a%29\",\r\n" );
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document.write( "where \"a\" is the coefficient of the profit function at x^2 and b is the coefficient at x.\r\n" );
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document.write( "In your case,  a= -1, b= 14;  therefore  \r\n" );
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document.write( "    \"x%5Bmax%5D\" = \"-14%2F%282%2A%28-1%29%29\" = \"14%2F2\" = 7.\r\n" );
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document.write( "Thus the number of containers that maximizes the profit is 7 thousands.\r\n" );
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document.write( "It is the  ANSWER  to question (b).\r\n" );
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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function see the lessons\r
\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.\r
\n" ); document.write( "\n" ); document.write( "Learn the subject from there once and for all.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Finding minimum/maximum of quadratic functions\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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