SOLUTION: An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function {{{P(x)=-10x^2+3500x-66000}}} Where

Question 231428: An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function Where P(x) is the profit in dollars and x is the number of automobiles made and sold. How many cars should be made and sold to maximize profits.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
What you have is a quadratic formula in the form of ax^2 + bx + c where:

a = -10
b = 3500
c = -66000

Since a is negative, this quadratic equation opens downward.

The max point is at x = -b/2a

That would be at x = -3500/-20 = 175.

When x = 175, y = -10*175^2 + 3500*175 - 66000 = 240250

Maximum profit attained is $240250.

This happens when 175 cars are sold.

graph of this equation looks like this:

As can be seen, the graph peaks at x = 175.

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