document.write( "Question 54340This question is from textbook Elementary and Intermediate Algebra
\n" ); document.write( ": The total profit (in dollars) for sales of x rowing machines is given by
\n" ); document.write( "P(x)=-0.2x^2+300x-200. What is the profit if 500 are sold? For what value of x will the profit be at a maximum? \n" ); document.write( "

Algebra.Com's Answer #36601 by funmath(2933) $\"\"$ $\"About$

You can put this solution on YOUR website!
For the first part substitute 500 in for x in the profit function:
\n" ); document.write( " $\"P%28x%29=-.2x%5E2%2B300x-200\"$
\n" ); document.write( " $\"P%28500%29=-.2%28500%29%5E2%2B300%28500%29-200\"$
\n" ); document.write( "=-.2(250,000)+300(500)-200
\n" ); document.write( "=-50,000+150,000-200
\n" ); document.write( " $\"highlight%28P%28500%29=99800%29\"$
\n" ); document.write( ":
\n" ); document.write( "For the second part, graphically, this is an upside down parabola. It's highest point is its vertex. The formula for finding the x value of a vertex of a parabola written in standard $\"highlight%28f%28x%29=ax%5E2%2Bbx%2Bc%29\"$ form is $\"highlight%28x=-b%2F%282a%29%29\"$
\n" ); document.write( "In your case a=-.2 and b=300, plug them into your formula and you have:
\n" ); document.write( " $\"x=-%28300%29%2F%282%28-.2%29%29\"$
\n" ); document.write( " $\"highlight%28x=750%29\"$
\n" ); document.write( ":
\n" ); document.write( "You weren't asked, but your maximum profit can be found by plugging in x=750 into your original equation P(750)=$112,300.
\n" ); document.write( "Happy Calculating!!!
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