Answer:
The data indicates: One flight has a total of 100 seats.
Full fare passengers, ticket cost=$150, average=56 passengers, SD=23.
Discount fare passengers, ticket cost=$100, average=88 passengers, SD=44.
(a) The question suggests optimizing total revenue per flight (one way) by potentially only taking full fare passengers, which would yield $15,000. However, historical probabilities show an average of 56 with a standard deviation of 23, thus in an ideal scenario, total full fare passengers could reach 79. That would allocate 21 tickets for discount passengers, leading to total revenues of $13,950.
(b) Now with the new constrained policy, specific seat allocations for both categories are set—44 for discount (resulting in total revenues of 44*100) and 56 for full fare (resulting in total revenues of 56*150)—both within the previously mentioned probabilities. The total revenue in this case will be 44*100+56*150 = $12,800.
(c) The difference in excess revenues between both scenarios for optimal total revenues and limited seats policy is calculated as answer (a) - answer (b) = $13,950 - $12,800 = $1,150.
(d) Realistically, this question cannot be properly answered without a clear confidence interval. Another simplifying assumption is to take the mean number of passengers as expected bookings (which can later be adjusted with provided confidence intervals). The total revenues in this scenario will come from 44*100 from discount and 56*150 from full fare passengers. This remains similar to answer (c) due to the assumption of no constraints, so optimal bookings might total 54 full fare tickets and 44 discount tickets. Worst case scenarios could involve subtracting SD from each passenger type’s mean, or for better scenarios, add SD of full fare passengers to the mean and allocate remaining seats for discount fare in order to maximize revenue.
