Marginal Révenue The demand function for a certain boat company's 34 ft Sundancer yacht is p = 900 – 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. R(x) = R'(x) = (b) Use the result of part (a) to estimate the revenue to be realized from the sale of the 450tn 34 ft Sundancer yacht (Round your answer to the nearest dollar.) $

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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**Marginal Revenue**

The demand function for a certain boat company's 34 ft Sundancer yacht is 

\[ p = 900 - 0.01x \ln(x) \]

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.

\[ R(x) = \]

\[ R'(x) = \]

**(b)** Use the result of part (a) to estimate the revenue to be realized from the sale of the \( 450^{th} \) 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 \[ p = 900 - 0.01x \ln(x) \] 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. \[ R(x) = \] \[ R'(x) = \] **(b)** Use the result of part (a) to estimate the revenue to be realized from the sale of the \( 450^{th} \) 34 ft Sundancer yacht. (Round your answer to the nearest dollar.) \[ \$ \]
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