please show explanations

OPRE. 3310: Homework Assignment 3 PLEASE PROVIDE EXPLANATIONS FOR ALL YOUR ANSWERS TO ENSURE YOU CAN RECEIVE PARTIAL CREDIT. CHATGPT USAGE IS STRICTLY FORBIDDEN! Q1 (9 points) Betty bakes and sells bagels all year round. Betty has to plan and manage inventories of paper take-out bags with her logo printed on them to satisfy customer demand. Daily demand for take-out bags is normally distributed with a mean of 90 bags and a standard deviation of 30 bags. Betty's printer charges her $10 per order for print setup independent of order size. Bags are printed at 5 cents ($0.05) each bag. It takes 4 days for an order to be printed and delivered. The annual inventory holding cost is $0.0125 per bag. Assume 360 days per year. (i) What is the optimal order quantity per order for Betty? (3 points) (ii) How many times per year does Betty need to order? (1 point) (iii) How many days will elapse between two consecutive orders? (I point) (iv) What is Betry's total annual cost of placing orders \& holding inventory? (2 points) (v) If Betty wants to make sure the bags do not run out with 99% probability during the order lead time, what is her optimal reorder point? (Use z 2.33 for 99% service level) (2 points)