Nadine is a student who receives money from her father in Switzerland. Her father has secured a yearly budget of $52000 for her daughter to pay for her studies and education. Unfortunately, Nadine overspends recklessly and occasionally runs short of money and overspends the money that she does not have in her account. The swiss bank charges the overspending as insufficient fund by $36 per $1000 per week. To allay this issue, the swiss bank has drafted a new policy in which it immediately informs Nadines father to send $1000 in replenishment for each $1000 that Nadine withdraws from her account. Sending $1000 each time by the father takes three weeks to be in Nadines account at virtually no cost. Nadine withdraws $1000 at a time and her average expenses during the three week replenishment time is estimated to be $3000 with a standard deviation of $!000 and is normally distributed..

a) What initial amount Nadines father should have deposited in her daughters account in the beginning of this new policy, in order to minimize his average banking costs?

b) What is optimal annual banking cost of his father in the new policy. Instead of a regular positive interest rate, in some Swiss banks, such as the one Nadine has account in, a negative interest rate is charged for providing security on positive account balance. The average negative interest cost is $20 per $1000 balance per week.