Suppose that all the assumptions of the EOQ derivation hold except that we now allow backorders (i.e., we deliberately let the stock level run negative before we order; backordered requests are completely filled out of the next replenishment). Now, there are two decision variables: Q and s (the level below zero at which we place an order).

a. Using a sketch and geometrical considerations, find the average on-hand inventory level and the average level of backorders.

b. Suppose that there is a cost B2v per unit backordered (independent of how long the unit is backordered) where B2 is a dimensionless factor. Find the best settings of Q and s as a function of A, D, v, r, and B2.

c. Repeat the previous part but now with a cost B3v per unit backordered per unit time.

The dimensions of B3 are equivalent to those for r.