Hello, If you could answer question 5 parts a-d showing step by step how you sol

Question

Hello,
If you could answer question 5 parts a-d showing step by step how you solved it so I may solve similar problems in the future myself, that would be greatly appreciated!
Thank you in advance! Question S: Airfare Revenue Maximization e tow tare. Low fare customers buy in advance of high fare customers. Demand for the ed with a mean of 100 and a standard deviation of 40. The high fare is The flight from Seattle t e ight from Seattle to Chicago has 250 seats, The airline offers a high and low fare. There is ample demand for the low fare. I high fare is Normally distributed with a $700 and the low fare is $450. ow fare customers a) What is the optimal protection level for the high fare? b) What is the total expected revenue (including both low and high-fare passengers) when the protection level is 110 seats?

Explanation / Answer

Solution:

a) Average demand = 250 Seats
Standard deviation = 40
Selling price (High Fare) = $700
Selling price (High Fare) = $450
The cost of bumping = $1500
The cost of underage Cu = 1500-450 = 1050
The cost of overage Co = 450
The critical ratio = 250/(250+450) = 0.3571.
Lookup the z-statistic in the Standard Normal Distribution Function Table that corresponds to the critical ratio: ( -0.36) = 0.3594, so choose z = -0.36. Q=100-0.36*40=85.6.

b) The excpected revenue when the protection level is 110 seats by using the following formula as given below.
Z = Protection level of seats- Mean/ Standard deviation
= 110-100/40
= 10/40 = 0.25
Using = NORMDIST(Z, 0, 1, 0)-0.25 * (1- NORMDIST (Z, 0, 1, 1))(0.25)
= 0.286345
Expected sales = 100-40*0.2863=88.5.Expected revenue = $700*88.5+$450*(250-110)=124,950.

c) Cost of underage Cu=450.
Cost of overage Co =1500.
The critical ratio=450/(450+1500) = 0.2308.
Lookup the protection level in the Poisson Distribution Table in the column corresponding to the mean of 9.5. Find that when Y =7, value in the table is 0.26866.
The maximum number of reservations to accept is 250+7=257.

d) If 20 seats are overbooked, a total of 320 seats are offered for sale. Furthermore 150 seats are protected for high-fare customers; then the booking limit for the low-fare customers is 320-150=170 seats.

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