document.write( "Question 1196413: A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of $1,500, 000 if successful and a
\n" ); document.write( "yearly loss of $500,000 otherwise. The probability of success is g. If the second mall is selected, it is estimated that the yearly profit will be $1.000,000 if successful,
\n" ); document.write( "otherwise, the annual loss will be $300,000. The probability of success at the second mall is g. Which mall should be chosen in order to maximize the expected profit? \n" ); document.write( "

Algebra.Com's Answer #829226 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A store specializing in mountain bikes is to open in one of two malls.
\n" ); document.write( "If the first mall is selected, the store anticipates a yearly profit
\n" ); document.write( "of $1,500, 000 if successful and a yearly loss of $500,000 otherwise.
\n" ); document.write( "The probability of success is g. \r
\n" ); document.write( "\n" ); document.write( "If the second mall is selected, it is estimated that the yearly profit
\n" ); document.write( "will be $1.000,000 if successful, otherwise, the annual loss will be $300,000.
\n" ); document.write( "The probability of success at the second mall is g. \r
\n" ); document.write( "\n" ); document.write( "Which mall should be chosen in order to maximize the expected profit?
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document.write( "To facilitate my writing and your reading, I will operate \r\n" );
document.write( "with the thousand dollars as my monetary unit. It allows me forget about \r\n" );
document.write( "three zeroes at the end of numbers.\r\n" );
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document.write( "Math expectation of yearly profit for 1st mall is  1500g - 500(1-g) units,\r\n" );
document.write( "which is  2000g - 500 units.\r\n" );
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document.write( "Math expectation of yearly profit for 2nd mall is  1000g - 300(1-g) units,\r\n" );
document.write( "which is  1300g - 300 units.\r\n" );
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document.write( "So, we need compare these two quantities/expressions\r\n" );
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document.write( "    2000g - 500  ?  1300g - 300.\r\n" );
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document.write( "Here the sign  \" ? \"  stands for one of two possible inequality signs  \" >= \"  or  \" <= \".\r\n" );
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document.write( "We transform it to\r\n" );
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document.write( "    2000g - 1300g  ?  500 - 300\r\n" );
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document.write( "         700g      ?     200\r\n" );
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document.write( "            g      ?      = .\r\n" );
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document.write( "Thus if g < 2/7, then 2nd mall gives greater Math expectation.\r\n" );
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document.write( "On contrary, if g > 2/7, then 1st mall gives greater Math expectation.\r\n" );
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document.write( "If g = 2/7, then Math expectations are the same for both malls.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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