question 3 & 4 please

Question 3 (Inventory Management I). [20 points] Rainbow Colors paint store uses a continuous review inventory system to control its stock levels. For a popular eggshell latex paint, historical data show that the distribution of monthly demand is approximately Normal, with mean 28 and standard deviation 8. Replenishment lead time for this paint is 2 months. Each can of paint costs the store $6. Fixed cost of replenishment is $15 per order and holding costs are based on a 30% annual interest rate. (1) What is the optimal lot size (economic order quantity) Q*? (2) What is the optimal reorder point (ROP) if Rainbow Colors wants to achieve a 90% cycle service level (i.e., Type I service level)? (3) Suppose the firm adopts a continuous review policy that uses the optimal Q* and ROP computed in (1) and (2). What is the Type II service level that corresponds to this policy? (4) Suppose the firm orders in the batch size of Q* computed in (1). What is the optimal reorder point (ROP) if Rainbow Colors wants to ensure that 90% of the demand are satisfied on time (i.e., Type II service level)