Suppose that we extend POQ model to the back order case. That is, the unfulfilled demand (the on-hand inventory is lower than the demand) is backlogged, and can be satisfied in future with a backlogging cost. The notations are defined as follows:

a)      Please draw a figure to describe the inventory levels at different time

b)      Please show the formula of the average total cost over a year

c)      To minimize the average total cost over a year, please determine the optimal Q and B