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

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) (Show Source): You can put this solution on YOUR website!
For the first part substitute 500 in for x in the profit function:

=-.2(250,000)+300(500)-200
=-50,000+150,000-200

:
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 form is
In your case a=-.2 and b=300, plug them into your formula and you have:

:
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!!!

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