The Audubon Society at Enormous State University (ESU) is planning its annual fu
ID: 1220203 • Letter: T
Question
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) = 380 + O.1Ox + 0.002x^2 dollars. Calculate the marginal revenue R'(x) and profit P'(x) functions. R'(x) = P'(x) = Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 200 servings of pasta, revenue $ Profit $ marginal revenue $ per additional plate marginal profit $ per additional plate Interpret the results. The approximate from the sale of the 201st plate of pasta is $ .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.Explanation / Answer
a)
TR=p.x=1.10x
R'(x)=1.10
P'(x)=TR-TC
=1.10q-380-0.10x-0.002x^2
b)x=200
TR=1.10*200=220
P'(x)=220-380-20-80=-260
MR=1.10
MC=0.1+0.004(200)=0.1+0.8=0.9
MR=1.10
marginal profit=1.1-0.9=0.2
marginal profit=0 when MC=MR=1.1
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