document.write( "Question 1144637: A fruit juice company varies the price of its litre cartons to maximise profit. The equation that models the company's profit is given below:
\n" ); document.write( "P=-80d^2+960d-2280
\n" ); document.write( "Where P is the profit in thousands of dollars and d is the price of a litre carton in dollars.
\n" ); document.write( "a) What is the maximum profit the company can make selling litre containers?
\n" ); document.write( "b) Sketch the general shape of the graph showing how profit varies with the price of a litre container.
\n" ); document.write( "c) What's the lowest price the company can sell litre cartons for and still break even? (Answer to the nearest 10 cents) \n" ); document.write( "

Algebra.Com's Answer #765808 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "(a)  Function  P(d) = - 80d^2 + 960d - 2280  is a quadratic function of the argument (variable) \"d\".\r\n" );
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document.write( "     For any quadratic function  f(x) = ax^2 + bx + c  with negative leading coefficient \"a\" at  x^2, \r\n" );
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document.write( "     its maximum is achieved at the value of   = .\r\n" );
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document.write( "     In your case,  a= -80,  b= 960.  Therefore\r\n" );
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document.write( "          =  =  = 6.\r\n" );
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document.write( "     \r\n" );
document.write( "      Thus the optimum price is  6 dollars (or whatever monetary units) per cartoon.\r\n" );
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document.write( "      It provides the maximum profit of  P(6) = -80*6^2 + 960*6 -2280 = 600 thousands of your monetary units.\r\n" );
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document.write( "(b)  Make a plot on your own.  //  When a \"student\" asks me to make a plot, I always think that it is his (or her) job - not my. \r\n" );
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document.write( "(c)  To answer this question, solve this quadratic equation\r\n" );
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document.write( "         P(d) = 0,  or  -80*d^2 + 960*d -2280 = 0.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function see the lessons in this site\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( "    - A rectangle with a given perimeter which has the maximal area is a square\r
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\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on finding the maximum/minimum of a quadratic function\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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