Sydney Garner is considering building a 300- seat amphitheater in a popular park. After studying the market, Sydney has drawn the following conclusions:

• There will be one show every night during summer months
• The theater will make a profit of $1 on each occupied seat and suffer a loss of $0.25 on each unoccupied seat.
• The probability that it rains on any given night is 0.2.
• The number of customers on a dry night is normally distributed, with a mean of 275 and a standard deviation of 30.
• The number of customers on a cold night is normally distributed, with a mean of 200 and a standard deviation of 50.

Set up Sydney's problem and simulate total profit for 1 month (30 days). In your model use integers for all demands. Replicate your model N times and calculate Sydney's average monthly profit.