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by C(x) = 60 + 0.10x + 0.001x2 dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x)

by C(x) = 60 + 0.10x + 0.001x2 dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.5: Graphical Differentiation
Problem 1E
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Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x copies of an edition is given by

C(x) = 60 + 0.10x + 0.001x2 dollars.
(a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.]
R'(x)  = 
 
 
 
P'(x)  = 
 
 
 


(b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition.
revenue     $ 
profit     $ 
marginal revenue     $  per additional copy
marginal profit     $  per additional copy

Interpret the results.
The approximate     from the sale of the 501st copy is $  .

(c) For which value of x is the marginal profit zero?
x =  copies

Interpret your answer.
The graph of the profit function is a parabola with a vertex at x =  , so the profit is at a maximum when you produce and sell  copies.
 
Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x copies of an edition is given by C(x) = 60 + 0.10x + 0.001x² dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) = 0.9 P'(x) = 0.8 – 0.002x (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition. revenue $ 450 profit $ 75 marginal revenue $ 0.9 V per additional copy marginal profit $ -0.20 per additional copy Interpret the results. The approximate loss from the sale of the 501st copy is $ 0.20 (c) For which value of x is the marginal profit zero? X = 400 сopies Interpret your answer. The graph of the profit function is a parabola with a vertex at x = 400 , so the profit is at a maximum when you produce and sell 400 copies.
Transcribed Image Text:Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x copies of an edition is given by C(x) = 60 + 0.10x + 0.001x² dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) = 0.9 P'(x) = 0.8 – 0.002x (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition. revenue $ 450 profit $ 75 marginal revenue $ 0.9 V per additional copy marginal profit $ -0.20 per additional copy Interpret the results. The approximate loss from the sale of the 501st copy is $ 0.20 (c) For which value of x is the marginal profit zero? X = 400 сopies Interpret your answer. The graph of the profit function is a parabola with a vertex at x = 400 , so the profit is at a maximum when you produce and sell 400 copies.
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Calculus For The Life Sciences
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
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