document.write( "Question 1173559: The Diver Time company makes digital watches for scuba divers. The company models its profits with
\n" ); document.write( "the function P(d) = −2d2+13d−6, where d is the number of watches sold, in hundreds, and P(d) is the
\n" ); document.write( "company’s profit, in tens of thousands of dollars.
\n" ); document.write( "a) How many watches does Diver Time need to sell to maximize profits?
\n" ); document.write( "b) What is the maximum profit? \n" ); document.write( "
Algebra.Com's Answer #798789 by ikleyn(52788)\"\" \"About 
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\n" ); document.write( "The Diver Time company makes digital watches for scuba divers. The company models its profits with
\n" ); document.write( "the function P(d) = −2d2+13d−6, where d is the number of watches sold, in hundreds, and P(d) is the
\n" ); document.write( "company’s profit, in tens of thousands of dollars.
\n" ); document.write( "a) How many watches does Diver Time need to sell to maximize profits?
\n" ); document.write( "b) What is the maximum profit?
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\n" ); document.write( "\n" ); document.write( "                    Part (a)\r
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document.write( "You are given a quadratic function  \r\n" );
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document.write( "    P(d) = -2d^2 + 13d - 6.    (1)\r\n" );
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document.write( "The function gas a negative leading coefficient -2 at the quadratic term d^2,  therefore, the function is a parabola\r\n" );
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document.write( "turned down.  It is very well known fact that such a quadratic function gets its maximum at the point\r\n" );
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document.write( "    d = \"-b%2F%282a%29\",\r\n" );
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document.write( "where \"a\" is the coefficient at the squared term and \"b\" is the coefficient at the linear term.\r\n" );
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document.write( "In your case  a= -2,  b= 13,  therefore the quadratic function gets its maximum value at\r\n" );
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document.write( "    \"d%5Bmax%5D\" = \"-13%2F%282%2A%28-2%29%29\" = \"13%2F4\" = 3.25\r\n" );
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document.write( "It means that the company should sell  \"13%2F4\"  hundreds of watches, or  325 watches.\r\n" );
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document.write( "Part (a) is completed and the answer is  3.25 hundreds of watches should be sold (or 325 watches).\r\n" );
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\n" ); document.write( "\n" ); document.write( "                    Part (b) \r
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document.write( "To find the maximum profit, substitute the found value of  \"d%5Bmax%5D\" = 3.25  into the formula (1)  to get\r\n" );
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document.write( "    \"P%5Bmax%5D\" = P(3.25) = -2*3.25^2 + 13*3.25 + 6 = 27.125  tens thousands of dollars, or $271,250.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. 325 watches should be sold to get the maximum profit of $271,250.\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
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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
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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
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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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