The Kelly Theater produces plays and musicals for a regional audience. For a typical$$ performance, the theater sells at least tickets and occasionally reaches its capacity of seats. Most$$ often, about tickets are sold. The fixed cost for each performance is normal with a mean of $$$ and a standard deviation of $$$$.$ Ticket prices range from $$$ to $$$ depending on the location of the seat. Of the $$seats$,$ are priced at $$$$,$ at $$$$,$ and the remaining at $$$$.$ Of all the tickets$$ sold, the $$$ seats sell out first. If the total demand is at least$500,$ then all the $$$ seats sell out. If$$ not, then between$50\%$ and$75\%$ of the $$$ seats$$ sell, with the remainder being the $$$ seats.$$ If$,$ however, the total demand is less than or equal to$350,$ then the number of $$$ and $$$ seats sold are usually split evenly. The theater runs performances per year and incurs an annual fixed cost of $$$ million. Develop a simulation model to evaluate the profitability of the theater using $50$ trials. What is the distribution of annual net profit and the risk of losing money over a$$ year?