Assume you are the manager of a hotel that has 330 rooms. You are trying to determine the price that will maximize the revenue.  You notice that as long as the hotel rate is $99 or lower, the hotel is fully booked. However if you raise the price above $99 you notice that for each $1 increase in price, two fewer rooms will be booked. For example if the hotel rate is $100, the number of rooms booked is 328,  if the hotel rate is $101, the number of rooms booked is 326, if the hotel rate is $102, the number of rooms booked is 324, and so on.  What price should you charge to maximize the revenue? Round your answer to the nearest integer. Your answer should be a whole number.

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...
icon
Related questions
Topic Video
Question

Assume you are the manager of a hotel that has 330 rooms. You are trying to determine the price that will maximize the revenue. 

You notice that as long as the hotel rate is $99 or lower, the hotel is fully booked. However if you raise the price above $99 you notice that for each $1 increase in price, two fewer rooms will be booked.

For example if the hotel rate is $100, the number of rooms booked is 328,  if the hotel rate is $101, the number of rooms booked is 326, if the hotel rate is $102, the number of rooms booked is 324, and so on. 

What price should you charge to maximize the revenue?

Round your answer to the nearest integer. Your answer should be a whole number.

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Knowledge Booster
Optimization
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning