Cory's dog, Jack, eats on average 3 lbs of dog food daily with a standard deviation of 0.5 pounds. Cory buys the food from an online shop that charges $2 per pound of food. The shop guarantees a 2-day delivery and the delivery fee is equal to $20. Cory doesn't have much storage space, so he estimates that keeping a pound of food in the cabinet essentially costs him $0.2 per week. The shop has two different sizes for food: 60 pound bags and 90 pound bags. Every time a new delivery arrives, Cory throws away any leftover food so that he doesn't mix new and old food. Also, if he runs out, he needs to replace the missing food with an equal amount of wet food which costs more, at $8 per pound. Note that z(0.75)=0.66.

a) Which size should Cory order every time he places an order?

b) What is Cory's annual holding cost?

c) What is Cory's annual ordering cost?

d) How many days after the previous delivery on average does Cory place an order?