Each year, Sherwin-Williams resells 20,000 cans of paint primer, which it purchases from a supplier for $1 per can. Each time Sherwin-Williams places an order, it incurs a ?xed cost of $100 for processing. Assume that the EOQ conditions hold, and that Nivek’s believes that un?lled orders can be backlogged (and ?lled at a later date) at a cost of $2 per can per month. Suppose also that the annual holding cost for surplus inventory is $4.80 per unit. Assume that, when a new shipment arrives from its supplier, Sherwin-Williams can ?ll backorders immediately.
(a) Determine the optimal order quantity.
(b) Using the optimal order quantity, determine the maximum shortage that will occur.
(c) Using the optimal order quantity, determine the fraction of time that there will be stockout (i.e., no positive inventory).