Please show all work including equations and stuff! And please make sure the answer is correct!

Q1. 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. Betty has a storage room big enough to hold all reasonable quantities of bags; its operating expenses may be regarded as fixed. The only holding cost is the opportunity cost of capital, which is estimated to be $0.0125 per unit per year. Assume 360 days per year. a. What is the optimal order quantity per order for Betty? (3 points) b. How many times per year does Betty need to order? (1 point) c. How many days will elapse between two consecutive orders? (1 point) d. What is Betty's total annual cost of placing orders & carrying inventory? (2 points) e. 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? (3 points)