document.write( "Question 1071427: Suppose that the price per unit in dollars of a cell phone production is modeled by p = $35 − 0.0125x,
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Algebra.Com's Answer #686394 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "Suppose that the price per unit in dollars of a cell phone production is modeled by p = $35 − 0.0125x,
\n" ); document.write( "where x is in thousands of phones produced, and the revenue represented by thousands of dollars is R = x · p.
\n" ); document.write( "Find the production level that will maximize revenue.
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document.write( "According to the condition, the revenue (measured in thousands of dollars) is \r\n" );
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document.write( "R(x) = x*(35-0.0125x),\r\n" );
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document.write( "where x is the number of the phones measured in thousand of units.\r\n" );
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document.write( "So, you need to find the maximum of this quadratic function\r\n" );
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document.write( "R(x) = -0.0125x^2 + 35x.\r\n" );
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document.write( "The maximum is achieved at x =   ( referring to the general form of a quadratic function q(x) =  ),\r\n" );
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document.write( "which at given conditions is x =  =  = 1400.\r\n" );
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document.write( "So, the maximum is achieved at the production level 1400 thousand of phone units .\r\n" );
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document.write( "The maximum revenue is the value R(x) at this value of x:\r\n" );
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document.write( " = R(1400) =  = 24500 thousands of dollars.\r\n" );
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document.write( "Answer.  The maximum revenue is 24500 thousands of dollars achieved at the production level of 1400 thousand of phone units .\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see other similar solved problems, see the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Using quadratic functions to solve problems on maximizing revenue/profit\r
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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( "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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