Please answer all parts in detail. Thank you.

Q1. Betty bakes and sells bagels all year round. Betty plans andmanages inventories of paper take-out bags with her logo printed onthem. Daily demand for take-out bags is normally distributed with amean of 90 bags and a standard deviation of 30 bags. Betty’sprinter charges her $10 per order for print setup independent oforder size. Bags are printed at 5 cents ($0.05) each bag. It takes4 days for an order to be printed and delivered. Betty has astorage room big enough to hold all reasonable quantities of bags.The holding cost is estimated to be 25% per year. Assume 360 daysper year. (Use the H= i × C formula to compute the annual holdingcost).

(a) What is the optimal order quantity per order for Betty?

(b) How many times per year does Betty need to order?

(c) How many days will elapse between two consecutiveorders?

(d) What is Betty’s total annual inventory-related cost (cost ofplacing orders and carrying inventory)?  

(e) What is the total cost per bag?

(f) What is Betty’s monthly inventory turns?

(g) If Betty wants to make sure the bags do not run out with 99%probability during the order lead time, what is her optimal reorderpoint? (Use z=2.33 for 99% service level)

(h) If Betty’s printer charges her $12 per order irrespective oforder size, what is the total annual inventory-related costs perbag?

(i) (Bonus) Assume that the print cost can bereduced to 3 cents per bag if Betty prints 9000 bags or more at atime. If Betty is interested in minimizing her total cost (i.e.,purchase and inventory-related costs), should she begin printing9000 or more bags at a time?