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

14019.999

Explanation:

Capacity(n) = 100

Ticket sold (t) = 120

Cost pet ticket (c) = $200

Unit cost (u) = $80 per passenger

Refund amount (r) = $300

Number of people who show up for the flight falls between 91 and 120

Total Revenue = t * c = (120 * $200) = $24,000

Total cost of operating flight per trip:

(u * n) = ($80 * 100) = $8,000

Profit = Revenue - cost

Since number of passengers who show up falls between 91 and 120

Take number who show up as 'p'

Case 1:

If 91 <= P <= 100, then the airline won't pay any refund, hence, profit = 24000 - 80p

Case 2:

If 100 < p <= 120, then refund will be made

Refund = 300 * (p - 100)

Profit = 24000 - 80p - (300p - 30000)

24000 - 8000 - 300p + 30000

Profit = 46000 - 300p

Expected profit :

n = (120 - 90)

Case 1

P= summation (91 to 0) = 955

(100 - 90) * (24000) - 80(955)

(20 * 24000) - 76400 = 163,600

163,600 / 30 = 5453.3333

Case 2:

P = summation (101 - 120) = 2210

(120 - 100) * (46000) - 300(2210))

(920,000 - 663,000) / 30

= 257,000 / 30 = 8566.6666

Case 1 + case 2

(8566.6666 + 5453.333= 14019.999