Question

Next week, super discount airlines has a flight from new york to los angeles that will be booked to capacity. the airline knows from past history that an average of 35 customers (with a standard deviation of 24) cancel their reservation or do not show for the flight. revenue from a ticket on the flight is $134. if the flight is overbooked, the airline has a policy of getting the customer on the next available flight and giving the person a free round-trip ticket on a future flight. the cost of this free round-trip ticket averages $263. super discount considers the cost of flying the plane from new york to los angeles a sunk cost. by how many seats should super discount overbook the flight? (use excel's normsinv() function to find the correct critical value for the given α-level. do not round intermediate calculations. round your answer to the nearest whole number.)

Answer 1

The cost of underestimating the demand is considered a revenue loss that arises due to cancellation of flight costing $134. Hence, cost of underetimating the demand is $C_u=\ 134$.

The cost of overestimating the demand is known as rewards. For example, free round trip ticket worth $263. Hence, the cost of overestimating the demand is $C_o=\ 263$.

$\frac{C_u}{C_u+C_o} = \frac{134}{134+263} \\ \\ = \frac{134}{397} =0.3375$

The z-score that yields a p-value of 0.3375 is -0.4193.

Thus, super discount airlines should overbook the flight by 35 + (-0.4193 x 24) = 35 - 10.0632 = 24.9368 = 25 seats.

Therefore, super discount airlines should overbook the flight by 25 seats.