Marginal Revenue The demand function for a certain boat company's 34 ft Sundancer yacht is p= 3000.01x In(x) where x denotes the number of yachts and p is the price per yacht in hundreds of dollars. (a) Find the revenue function R(x) and the marginal revenue function R'(x) for this model of yacht. R(x) = 300x -0.01x²ln(x) ✔ Exactly! R'(x) = -0.01x -0.02x ln(x) + 300 ✓ Exactly! (b) Use the result of part (a) to estimate the revenue to be realized from the sale of the 225th 34 ft Sundancer yacht. (Round your answer to the nearest dollar.) $

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.4: Combining And Decomposing Functions
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Marginal Revenue The demand function for a certain boat company's 34 ft Sundancer yacht is
p = 300 0.01x In(x)
where x denotes the number of yachts and p is the price per yacht in hundreds of dollars.
(a) Find the revenue function R(x) and the marginal revenue function R'(x) for this model of yacht.
300x -0.01x²ln(x)
-0.01x -0.02x ln(x) + 300
R(x)
R'(x)
=
=
Exactly!
Exactly!
(b) Use the result of part (a) to estimate the revenue to be realized from the sale of the 225th 34 ft Sundancer yacht. (Round your answer to the nearest dollar.)
$
Transcribed Image Text:Marginal Revenue The demand function for a certain boat company's 34 ft Sundancer yacht is p = 300 0.01x In(x) where x denotes the number of yachts and p is the price per yacht in hundreds of dollars. (a) Find the revenue function R(x) and the marginal revenue function R'(x) for this model of yacht. 300x -0.01x²ln(x) -0.01x -0.02x ln(x) + 300 R(x) R'(x) = = Exactly! Exactly! (b) Use the result of part (a) to estimate the revenue to be realized from the sale of the 225th 34 ft Sundancer yacht. (Round your answer to the nearest dollar.) $
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