SOLUTION: P(x) = -.2x^2 +300x-200. What is the profit if 500 are sold? What value of x will the profit be at a maximum?

Question 97347: P(x) = -.2x^2 +300x-200. What is the profit if 500 are sold? What value of x will the profit be at a maximum?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given polynomial

Plug in

Evaluate to get 250,000

Multiply -.2 and 250,000 to get -50,000

Multiply 300 and 500 to get 150,000

Combine like terms

So when 500 are sold, the profit is $99,800

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To find the maximum x-value, you simply need to find the axis of symmetry. So the axis of symmetry is:

where b is the x-coefficient and a is the coefficient

Plug in a=-.2 and b=300

Multiply

Divide

So when 750 are sold, the profit is at the maximum
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