Alliance Air is a service in which customers pay a flat-rate to Alliance Air and are guaranteed a seat on an airplane between any two locations. To offer this service, Alliance Air prepurchases daily seats between every pair of major cities. A route which has been growing in popularity is between Phoenix and Dallas and Alliance Air is seeking your advice on how many seats to prepurchase between these two cities so that they maximize their daily profit.

Whenever an Alliance Air customer flies on a prepurchased seat, Alliance Air obtains $100 in profits. If not all of the prepurchased seats are taken, then Alliance Air looses $20 in profit by selling their seats at a discount to passengers outside of their customer base. However, if Alliance Air has more customers seeking a seat than they have prepurchased, Alliance Air is forced to book that passenger on a seat purchased that day. In this case, Alliance Air looses $170 in profit per same-day seat due to the high cost of same-day flights. Based on their data, Alliance Air knows that number of customers seeking a flight on any day follows a Poisson distribution with a mean of 40.

Using this information, complete the following tasks/questions:

1. Develop an Excel spreadsheet model which can calculate the daily profits for Alliance Air, assuming any particular demand for that day and that Alliance Air pre-purchased 37 seats on the plane. Hint: Your model should include an understock and an overstock formulas.

1. Using the given demand distribution, set-up your spreadsheet as a simulation model using daily profits as the output. Run the simulation assuming Alliance Air pre-purchased 37 seats on the plane. What is the average daily profit in this scenario?
2. How many seats would you recommend Alliance Air to pre-purchase if they wanted to maximize their average daily profit? To answer this question, modify the number of Pre-Purchased Daily Seats from 30 to 55 (in the increments of 5) and fill in the table provided with statistics about the expected daily profits (Note that the average, min and max might keep changing slightly as you record those values, thats ok). What are the minimum and maximum daily profits if they were to purchase this quantity?

$ $ $ 100 Pre-Purcha Avg Profit Min Profit Max Profit 80 (170) Alliance Air Service Prepurchased Seat Full Profit Discounted Flight Sale Same Day Flight Average Demand Pre-Purchased Flights Seats Sold for Full Profit Discounted Flights Sold Same Day Flights to purchase Daily Profit