Question 54340
For the first part substitute 500 in for x in the profit function:
{{{P(x)=-.2x^2+300x-200}}}
{{{P(500)=-.2(500)^2+300(500)-200}}}
=-.2(250,000)+300(500)-200
=-50,000+150,000-200
{{{highlight(P(500)=99800)}}}
:
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(f(x)=ax^2+bx+c)}}}form is {{{highlight(x=-b/(2a))}}}
In your case a=-.2 and b=300, plug them into your formula and you have:
{{{x=-(300)/(2(-.2))}}}
{{{highlight(x=750)}}}
:
You weren't asked, but your maximum profit can be found by plugging in x=750 into your original equation P(750)=$112,300.
Happy Calculating!!!