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) = 40 + 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 $ 44,660 marginal revenue $ 90 X per additional copy marginal profit $ 90.9 X per additional copy Interpret the results. The approximate loss Ov from the sale of the 501st copy is $ 304 (c) For which value of x is the marginal profit zero? x copies X= 44950 Interpret your answer. The graph of the profit function is a parabola with a vertex at x = 44950 X , so the profit is at a maximum when you produce and sell 44950 X copies.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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) = 40 + 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
$ 44,660
marginal revenue
$ 90
X per additional copy
marginal profit
$ 90.9
X per additional copy
Interpret the results.
The approximate
loss
from the sale of the 501st copy is $ 304
(c) For which value of x is the marginal profit zero?
X = 44950
X copies
Interpret your answer.
The graph of the profit function is a parabola with a vertex at x = 44950
, so the profit is at a maximum when you produce and sell 44950
X 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) = 40 + 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 $ 44,660 marginal revenue $ 90 X per additional copy marginal profit $ 90.9 X per additional copy Interpret the results. The approximate loss from the sale of the 501st copy is $ 304 (c) For which value of x is the marginal profit zero? X = 44950 X copies Interpret your answer. The graph of the profit function is a parabola with a vertex at x = 44950 , so the profit is at a maximum when you produce and sell 44950 X copies.
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