Explanation Given information: A cruise line offers a trip for $2000 per passenger. If at least 100 passengers sign up, the price is reduced for all the passengers by $10 for every additional passenger. The boat can accommodate 250 passengers. Calculation: Let n be the number of passengers then the total revenue for the cruise ship is given by R = q . p = ( 2000 − 10 ( n − 100 ) ) n = 2000 n − 10 n 2 + 1000 n R = 3000 n − 10 n 2 Differentiating with respect to ‘n’, we get R ' = 3000 − 20 n For the critical points, R ' = 0 ⇒ 3000 − 20 n = 0 ⇒ n = 3000 20 ⇒ n To determine (b) To find: The maximum profit that the cruise line can make on the trip, the number of passengers must sign up for the maximum to be reached and the price will each pay.

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Question

Chapter 4.4, Problem 32P

To determine

(a)

To find:

The number of passengers maximizes the cruise line’s total revenue and the price that each passengerpays then.

To determine

(b)

To find:

The maximum profit that the cruise line can make on the trip, the number of passengers must sign up for the maximum to be reached and the price will each pay.

Expert Solution & Answer

Chapter 4 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

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(a) To find: The number of passengers maximizes the cruise line’s total revenue and the price that each passengerpays then.

Solution Summary: The author analyzes how the number of passengers maximizes the cruise line's total revenue and the price that each passenger pays then.

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(a) To find: The number of passengers maximizes the cruise line’s total revenue and the price that each passengerpays then.

(b) To find: The maximum profit that the cruise line can make on the trip, the number of passengers must sign up for the maximum to be reached and the price will each pay.

Chapter 4 Solutions

(a)

To find:

The number of passengers maximizes the cruise line’s total revenue and the price that each passengerpays then.

(b)

To find:

The maximum profit that the cruise line can make on the trip, the number of passengers must sign up for the maximum to be reached and the price will each pay.