At this stage of the contract, AA's operations manager must specify the seating configuration on the airplane that will be used on the Charlotte - Miami - New York City - Charlotte circuit. AA flies this circuit once per day.

The configuration decision involves specifying how many rows will be allocated for business-class seats and how many for coach seats. Each business-class row contains 4 seats and each coach row contains 6 seats. If the aircraft were configured entirely of coach rows, there would be 40 rows. Business-class seats are wider and afford more legroom, so that, in order to make room for one business-class row, two coach rows must be removed. Thus, conversion from coach to business-class seating involves the loss of some seats, but this loss might be compensated from the higher prices paid by the business-class passengers. The revenues rates for business-class and coach seats are given below.

Table 1: Revenue per Seat

	Business-class	Coach
Charlotte - Miami	$550	$300
Miami - New York City	$400	175
New York City - Charlotte	$450	$200

A perfect match between the configuration and the demand for seats is seldom possible. Historical data suggests a probability of demand for seats on each leg (as detailed below).

Table 2: Distribution of Total Demand for Seats

	Minimum	Most Likely	Maximum
Charlotte - Miami	160	180	220
Miami - New York City	140	200	240
New York City - Charlotte	150	200	225

There is another distribution for the fraction of demand that corresponds to business-class seats (given below). While demand seems to vary on each leg of the circuit, this distribution offraction applies on all legs. It is assumed that if a passenger cannot book a seat in the seating category he/she intends to book, then he/she will simply buy a seat from AA's competitors.

Table 3: Distribution of Fraction Business Class

Fraction of Business-Class	Probability
5%	0.2
12%	0.5
15%	0.3

The fixed cost of operating the airplane is $125,000 per day for the full circuit. AA is seeking a profit-maximizing configuration.

Questions:

1. (20 pts) Suppose that AA is considering a plane configuration that has 3 rows of business-class seats and 34 rows of coach seats. Create a spreadsheet model for this problem and replicate it 1000 times.

a1) What is the minimum, average, maximum profit per day for this configuration?

a2) What is the probability that AA will earn a positive profit on this circuit? Establish a 95% confidence interval for the probability of AA earning a positive profit on this circuit.

A3) What is the optimal seat configuration that maximizes AA's expected profit from the circuit? Use psi sim param function to find the answer