The manager of a local movie theater has asked you to develop a spreadsheet that will help her to estimate total expected daily revenue for the theater. The theater consists of 200 seats, and has 5 show times daily (3 matineee, 2 evening shows). On any given day, approximately 40% of all ticket sales arise from matinee shows. The price of a matinee is $9, and the average price of an evening show is $14. From ticket sales data, the manager has estimated that the average demand for tickets is 850 per day. However, due to theater capacity, this demand level does not always convert to the same level of ticket sales. Another stream of revenue for the theater is concession sales. Based on past receipts, the manager computes the average patron expenditure for concessions as $12, and estimates the 50% of patrons purchase concessions.

1. Construct a chart to display how Daily Total Revenue varies as Daily Demand increases from 100 to 700. What do you observe from the chart produced?

2. Modify the model the below model to incorporate the following random variables:
Inputs
	Seating Capacity	200	seats per show
	Matinee showings	3
	Evening showings	2
	Matinee % of tickets	40%
	Matinee avg ticket price	$9	per seat
	Evening avg ticket price	$14	per seat
	Avg consession sale	$12
	Patron % concessions	50%
	Average demand per day	850	seats
Demand vs Capacity
		ticket demand	capacity	tickets sold
	Matinee	340	600	340
	Evening	510	400	400
Revenue Computation
	Matinee ticket sales	$3,060.00	per day
	Evening ticket sales	$5,600.00	per day
	Concession sales	$4,440.00	per day
	Total revenue	$13,100.00	per day

Matinee % of tickets follows a Uniform (25%, 55%) distribution

Average Concession Sales follows a Normal ($12, $2.50) distribution

Average Demand per Day follows a Normal (850, 250) distribution rounded to integer values

3. Simulate at least 500 tirals of this sytem and answer the following questions based on the results of your simulation.

What is the expected value of total daily revenue?

What is the 95% confidence internval for the expected value of total daily revenue?

What is the probability that total daily revenue will exceed $15000?

Assume the daily total cost of operating the theater is $10000. What is the probability that the daily profit will fail to be positive?