Suppose a construction materials company sells gravel for road construction projects. They order gravel periodically from their supplier using a continuous review policy. The average demand is 320 cubic yards per day with a standard deviation of 50 per day. Suppose the lead time from their supplier varies with an average of 10 days with a standard deviation of 3 days. The construction materials company operates 365 days a year.

a) If a 95% service level is desired, then what would be the reorder point? Show all your work. Reorder point = ________  

b) Suppose each gravel order from the construction materials company to its supplier is for 3000 cubic yards. With that order size, how many orders do they make per year? Show all your work. Number of orders per year = ________

c) Suppose each gravel order from the construction materials company to its supplier is for 3000 cubic yards. With that order size, and with a 90% service level, on average how many stockouts do they expect in a year? Show all your work. Stockouts per year = ________