Athens Gas Station has figured out the weekly demand distribution for their gas sales. Each gallon of gas sold at the pump results in a profit of 10 cents/gallon and any lost sales results in a cost of 15 cents/gallon. The gas station at present has 2000 gallons in storage. The storage capacity is 5500 gallons. Any excess gas above the storage capacity is shipped back to the distributor at a cost of $2 cents/gallon. Simulate the demand for 40 weeks.

Demand	Probability
2000	0.12
3000	0.23
4000	0.48
5000	0.17

a) What is the average weekly demand, sales, shortage and ship back quantities? What are the corresponding average weekly costs and profits?

b) Vary the order quantity to figure out the one that results in highest average weekly profit. Plot a chart of order quantity and profit to make your point.