Migros supermarket provides Olive Oil to its customers. Each liter for the supermarket costs 40 TL. The shipping cost per order, regardless of the size, is 200 TL, and receiving an order costs 50 TL. Each order takes 4 months to arrive. The supermarket calculates holding costs based on the cost of capital at 15% per year. Suppose the demand for the product is not known in advance and follows a normal distribution with a mean of 350 liters per month and a standard deviation of 50 liters per month. Furthermore, backordering costs are calculated at 28 TL per liter per year.

a)Calculate the optimal order quantity and reorder level if the supermarket wants to apply a (Q, R) policy.

b) For the optimal policy in part(a), what are the type-I and type-II service levels?

c) Suppose the backordering cost is not known, and the supermarket aims to find an inventory policy with a 90% type-I service level. Find the optimal (Q, R) values under this policy.