Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 10.5, Problem 34E

(a)

To determine

To find: The ticket price should the airline charge to achieve the greatest income on an average flight, based on the given estimates.

(a)

Expert Solution

Answer to Problem 34E

Max at 97.50 dollars

Explanation of Solution

Given information: Business: An airline has been charging $140 per seat for a one-way flight. This flight has been averaging 110 passengers but can transport up to 180 passengers. The airline is considering a decrease in the price for a one-way ticket during the winter months. The airline estimates that for each $10 decrease in the ticket price, they will gain approximately 20 passengers per flight.

Calculation:

Income = (passengers) (price)

=(110+20x)(140−10x)=15,400+1700x−200x2

Vertex at: (−1700−400)=4.25

Thus,

Max at 97.50 dollars

(b)

To determine

To find: The new ticket price, to maximize income. New estimates reveal that the increase in passengers per flight is closer to 10 for each $10 decrease in the original ticket price.

(b)

Expert Solution

Answer to Problem 34E

Max at 125 dollars

Explanation of Solution

Calculation:

Income: (110+10x)(140−10x)=

15,400+300x−100x2

Maximum at: −300−200=1.5

Thus, max at 125 dollars.

Chapter 10.5, Problem 33E

Chapter 10.5, Problem 35E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFU Ch. 10.1 - Prob. 2CFU Ch. 10.1 - Prob. 3CFU Ch. 10.1 - Prob. 4CFU Ch. 10.1 - Prob. 5CFU Ch. 10.1 - Prob. 6CFU Ch. 10.1 - Prob. 7CFU Ch. 10.1 - Prob. 8CFU Ch. 10.1 - Prob. 9CFU Ch. 10.1 - Prob. 10CFU

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