The Kelly Theater produces plays and musicals for a regional audience. For a typical performance, the theater sells at least 250 tickets and occasionally reaches its capacity of 600 seats. Most often, about 450 tickets are sold. The fixed cost for each performance is normal with a mean of $2,500 and a standard deviation of

$250. Ticket prices range from $30 to $70 depending on the location of the seat. Of the 600 seats, 150 are priced at $70, 200 at $55, and the remaining at $30.

Of all the tickets sold, the $55 seats sell out first. If the total demand is at least 500, then all the $70 seats sell out. If not, then between 50% and 75% of the $70 seats sell, with the remainder being the $30 seats. If, however, the total demand is less than or equal to 350, then the number of $70 and $30 seats sold are usually split evenly. The theater runs 160 performances per year and incurs an annual fixed cost of $2 million. Develop a simulation model to evaluate the profitability of the theater. What is the distribution of net profit and the risk of losing money over a year?