Six months before an annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $150 per room. The AMA believes that number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending exceeds the number of rooms reserved, extra rooms must be reserve at cost for $2500 per room. Early reservations are non-refundable.

a.Formulate an expression to calculate the total lodging cost for AMA. Explain your notation and identify uncertain inputs

b.You built a simulation model that calculates total lodging cost with 5000 early reservations (at a cost $150 each) and based on 1,000 iterations obtain the following distribution of total lodging cost:.

Explain the shape of the distribution. Why is there a spike on the left?

c. Now, assume you use the RiskSimTable() function to test multiple values of early reservations, ranging from 3500 to 7,000 in increments of 500, and compute the Mean, and Standard Deviation of total cost. The simulated table is given below:

Given this table, how many rooms should be reserved (assume risk-neutral decision maker)?

If the decision-maker is risk averse, how many rooms should be reserved? Explain your selection.

Total Cost 1.160 0.750 90.0% 5.0% 2.5 2.0 1.5 Values x 10^-5 @RISK Course Version University of Maryland 1.0 0.5 0.0 o 0.8 60 1.0 : 1.3 1.4 1.5 - 1.6 Values in Millions