Pete owns a small business renting out bicycles in Vancouver. He rents each bike for $5 a day. After a year, his rental bikes are worn out and basically worthless. So each year Pete gives his old bikes to a local charity and replaces his entire fleet of bikes. Pete buys his bikes from a local manufacturer at the discounted price of $500 each. Pete has estimated the following probability distribution of the number of bikes he can expect to rent on any given day:

Number of bikes rented per day	10	11	12	13	14
Probability	0.10	0.25	0.40	0.20	0.05

After Pete rents out a bike, he has to clean and tune it before he can rent it out again. The average cost of this maintenance is $2 per bike. This includes the cost of materials and the opportunity cost of Petes time. Petes store is open five days a week year-round, except during a four-week period each January when he goes skiing. How many bikes should Pete buy each year to maximize his expected profit?