Chicago's Hard Rock Hotel distributes a mean of $1,000$ bath towels per day to guests at the pool and in their rooms. This demand is normally distributed with a standard deviation of

$95$ towels per day, based on occupancy. The laundry firm that has the linen contract requires a $4-$day lead time. The hotel expects a $96\%$ service level to satisfy high guest

expectations. Refer to the standard normal table for z$-$values.

a$)$ What is the reorder point? towels $($round your response to the nearest whole number$).$

b$)$ what is the overage cost per program?

c$)$ how many programs should be ordered per game?

d$)$ what is the stockout risk for this order size?