George’s 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 George buy each year to maximize his expected profit? 

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

After George 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 George’s time.
George’s 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 George buy each year to maximize his expected profit?