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Chapter 1: Problem 40

An airplane can hold 325 passengers, 30 in first class and the rest in coach. If a first-class ticket costs \(700 and a coach ticket costs \)250, then what is the minimum revenue that the airplane will gross on a flight in which exactly 3 seats remain empty?

Short Answer

Expert verified
The minimum gross revenue on a flight with exactly 3 empty seats is $92,650.

Step by step solution

01

Determine the number of coach seats and first-class seats with 3 empty seats

If 30 seats are for first-class passengers and the rest are coach, then there are 325 - 30 = 295 coach seats on the airplane. We are given that exactly 3 seats remain empty, so we'll assume these empty seats are in first-class to minimize revenue. Therefore, there are 30 - 3 = 27 first-class seats occupied.
02

Calculate the revenue from the occupied first-class seats

Each first-class ticket costs \(700. So, the revenue from the first-class tickets is 27 * \)700 = $18,900.
03

Calculate the revenue from the occupied coach seats

Assuming all coach seats are occupied, there are 295 occupied coach seats. Each coach ticket costs \(250, so the total revenue from coach tickets is 295 * \)250 = $73,750.
04

Calculate the total minimum revenue

To find the total minimum revenue, add the revenue from occupied first-class and coach seats: \(18,900 + \)73,750 = $92,650. The minimum gross revenue on a flight with exactly 3 empty seats is $92,650.

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