SOLUTION: The total profit (in dollars) for sales of x rowing machines is given by 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

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Question 54340This question is from textbook Elementary and Intermediate Algebra
: The total profit (in dollars) for sales of x rowing machines is given by
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? This question is from textbook Elementary and Intermediate Algebra

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
For the first part substitute 500 in for x in the profit function:
P%28x%29=-.2x%5E2%2B300x-200
P%28500%29=-.2%28500%29%5E2%2B300%28500%29-200
=-.2(250,000)+300(500)-200
=-50,000+150,000-200
highlight%28P%28500%29=99800%29
:
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%29form is highlight%28x=-b%2F%282a%29%29
In your case a=-.2 and b=300, plug them into your formula and you have:
x=-%28300%29%2F%282%28-.2%29%29
highlight%28x=750%29
:
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!!!