The Richardson hospital consumes 500 boxes of masks on average each week. The The price of each box is $50. The cost of placing an order is $250, and the cost of holding a box for a year is 1% of the value of the box. Assume 50 weeks per year. The demand is normally distributed with a standard deviation of 100 boxes (the mean is 500 as indicated before). The lead time is week. Please show work.

1. What is the total cost of carrying inventory and placing orders?

2. Suppose that the hospital wants to keep a safety stock of 50 boxes. What would be the re-ordering point?

3. Suppose that the hospital wants to guarantee a service level of 95%. What should be the re-ordering point?

[Round your answer down to the nearest integer value. For example, 2.3 and 2.6 both should be rounded down to 2.]