Question

An airline sells 120 tickets for a flight that seats 100. Each ticket is non-refundable and costs $200. The unit cost of flying a passenger (fuel, food, etc.) is $80. If the flight is overbooked, each person who does not find a seat is given $300 in cash. Assume it is equally likely that any number of people between 91 and 120 show up for the flight. Rounded to the nearest thousand (e.g., 18500 rounds to 19000), on the average how much expected profit (ignoring fixed cost) will the flight generate? Enter just the number; e.g., 11000.

Answer 1

total profit gained by airline = $14000

Step-by-step explanation:

Given data:

total ticket sell 120

per ticket cost $200

total earning by selling = 12*200 = $24,000

unit cost of flying a passenger is $80

cost of flying for 100 passeneger = $80*100 = $8000

let x is the number of passenger between 91 and 100

if 91\leq x\leq 100 , therefore all passenger get the seat

hence profit of the airline is
`24000  - 80* x`

if
`101\leq x \leq 120` then (x-100) will not get the seat

therefore airline has to pay $300(x-100)

profit for the airline will be = 24000 - 8000 - 300(x-100)

= $46000 - $300x

for average profit to the airline, add from 91 to 120 and divide by 120 to 92=1

`= (1)/(30)( \sum_(91)^(100) (24000 - 80x ) + \sum_(101)^(120)(46000 - 3000x))`

after solving we get

= $14020

= $14000