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

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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 P%28x%29=-10x%5E2%2B3500x-66000 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) About Me  (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:

graph%28400%2C400%2C-50%2C350%2C-100000%2C300000%2C-10x%5E2%2B3500x-66000%2C240250%29

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