9)

The Audubon Society at Enormous State University (ESU) is planning its annual fund-raising "Eatathon." The society will charge students $1.10 per serving of pasta. The society estimates that the total cost of producing x servings of pasta at the event will be

C(x) = 350 + 0.10x + 0.002x² dollars.

(a)

Calculate the marginal revenue R'(x) and profit P'(x) functions.

R'(x)=

P'(x)=

(b)

Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 200 servings of pasta (in $).

revenue$_________

profit$__________

marginal revenue$__________ per additional plate

marginal profit$____________ per additional plate

Interpret the results.

The approximate ---Select--- (profit, loss )from the sale of the 201^st plate of pasta is $__________ .

(c)

For which value of x is the marginal profit zero?

x = ________ plates

Interpret your answer.

The graph of the profit function is a parabola with a vertex at x =__________ , so the loss is at a minimum when you produce and sell ________ plates.