For each problem, make an Excel model, simulate via YASAI, and hand in the standard printouts for a simulation problem.
 

Q1. (40 points)  Remote Airlines operates flight 502 with an aircraft which, if configured for all passengers, the aircraft holds 216 seats. The airline can set up the interior of the aircraft to have space to hold up to 0, 1, 2, 3, 4, 5, or 6 freight pallets. To make room for each pallet, the airline must remove 24 seats.  Demand for passenger seats is described by a Poisson random variable with mean value 160, and the airline makes a profit of $50 per occupied seat. Demand to transport freight pallets is independent of the demand for passenger seats, and has historically followed the following distribution:

The airline makes a profit of $275 per pallet carried. Unfortunately, the aircraft cannot be reconfigured for each flight. The split between seats and space for pallets must be decided once a year when the aircraft undergoes "heavy maintenance". What aircraft configuration maximizes the average profit per flight? Simulate 1000 flights for each possible configuration.
 

Q2. (60 points)   You make a perishable, volatile chemical for which you charge $2.25 per liter.  You have 75 regular customers for the chemical, each of whom has an independent 90% chance of placing an order on any given day.  You also get an average of 33 orders per day from other, non-regular customers; assume the number of non-regular customers per day has a Poisson distribution.  

The chemical may be ordered in any amount down to fractions of liters.  The amount ordered by each customer is independent, has a mean of 20 liters, and a standard deviation of 12 liters.

You produce the chemical by two batch processes, called "large" and "small".  The large batch process produces 800 liters of the chemical at a cost of $1300, while the small batch process produces 500 liters at a cost of $850.  Each day, you can run each of these processes any whole number of times.  Because it is so unstable, any chemical left unsold at the end of the day must be recycled, at a cost of $0.35 per liter. 

What is the best number of times to run each process?  Use a sample size of 1000 and consider all nine possible combinations of running the large process either 1, 2, or 3 times, and the small process either 0, 1, or 2 times.  For the choice giving the highest average profit per day, what is the average number of liters recycled per day?