document.write( "Question 691277: A chain store manager has been told by the main office that the daily profit, P, is related to the number of clerks working that day,x, according to the function \r
\n" ); document.write( "\n" ); document.write( "P = -25x^2 + 300x\r
\n" ); document.write( "\n" ); document.write( "What number of clerks will maximize the profit, and what is the maximum possible profit?
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Algebra.Com's Answer #426621 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The minus in front of the $\"+x%5E2+\"$ term
\n" ); document.write( "means there is a max and not a min.
\n" ); document.write( " $\"+P+=+-25x%5E2+%2B+300x+\"$
\n" ); document.write( " $\"+P+=+x%2A%28+300+-+25x+%29+\"$
\n" ); document.write( "Set $\"+P=0+\"$ to find roots
\n" ); document.write( "the roots are
\n" ); document.write( " $\"+x+=+0+\"$
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\n" ); document.write( " $\"+300+-+25x+=+0+\"$
\n" ); document.write( " $\"+25x+=+300+\"$
\n" ); document.write( " $\"+x+=+12+\"$
\n" ); document.write( "-----------
\n" ); document.write( "The x-coordinate of the maximum
\n" ); document.write( "is midway between the roots
\n" ); document.write( " $\"+%28+0+%2B+12+%29+%2F+2+=+6+\"$
\n" ); document.write( "So $\"+x+=+6+\"$ is the maximum
\n" ); document.write( "Now find $\"P\"$ at $\"+x=6+\"$
\n" ); document.write( " $\"+P+=+-25%2A6%5E2+%2B+300%2A6+\"$
\n" ); document.write( " $\"+P+=+-900+%2B+1800+\"$
\n" ); document.write( " $\"+P+=+900+\"$
\n" ); document.write( "With 6 clerks working that day, there is
\n" ); document.write( "a maximum profit of $900
\n" ); document.write( "here's a plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-2%2C+15%2C+-50%2C+1000+%2C+-25x%5E2+%2B+300x+%29+\"$ \r
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