(a) Consider the inventory policy with constant demand D units per unit time and uniform replenishment at a rate of >D. Assume the setup cost is $K per order, and the holding cost is $h per unit inventory per unit time. (i) If no shortage is allowed, derive the economic order quantity formula by considering the inventory plot and total cost per unit time. (ii) Show that the EOQ under instantancous replenishment can be derived from the formula in (i). (iii) If shortage is allowed at a penalty cost of $p per unit inventory per unit time, derive the maximum shortage quantity that minimizes the total cost per unit time