The profit function of a manufacturer, in dollars, when x units of a certain commodity are produced and sold is given by P(x)=200x−x2.

(a) The maximum profit is
dollars.

(b) The number of units produced and sold to get the maximum profit is
units.

Derivative: P’(x) = 200 - 2x

If P’(x) = 0 , x = 100

Therefore P’ is positive and P increases until x = 100

So the maximum units to maximize profits is 100 units

And for 100 units the profit in dollar is:

20000 - 10000 = 10000

10000 dollars

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step-by-step explanation: