document.write( "Question 136931: I have several word problems to solve but this is the first one. John owns a hotdog stand. His profit is represented by the equation P(x)=-x^2+12x+46, with P being profits and the x the number of hotdogs sold. What is the most he can earn? \n" ); document.write( "

Algebra.Com's Answer #100217 by dolly(163) $\"\"$ $\"About$

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Hi,\r
\n" ); document.write( "\n" ); document.write( "The most he can earn is basically the maximum value of the function.
\n" ); document.write( "And the maximum occurs at the vertex of this parabola.\r
\n" ); document.write( "\n" ); document.write( "The given equation is P(x) = -x^2+12x+46,\r
\n" ); document.write( "\n" ); document.write( "The x coordinate of the vertex = $\"%28-b%29%2F%282%2Aa%29\"$ \r
\n" ); document.write( "\n" ); document.write( " = $\"%28-12%29%2F%282%2A%28-1%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " = 6\r
\n" ); document.write( "\n" ); document.write( "Plugging this value of x in P(x), P(6)= -36 + 72 + 46
\n" ); document.write( " = 82\r
\n" ); document.write( "\n" ); document.write( "Thus the most he can earn is 82 \r
\n" ); document.write( "\n" ); document.write( "Good luck!!!\r
\n" ); document.write( "\n" ); document.write( "dolly\r
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