Each year, a company uses half a million Rials worth of a highly toxic product costing OMR 50 per drum. Orders costs OMR 4 each and there no limit on the storage capacity.
However the dangers of an explosion are such that the company's insurers insist on higher premiums if the product is stocked in large quantities. The effect of this is that the annual holding rate is only 4% if the average stock does not exceed 20 drums but is 25% ifthe average stock is greater than 40 drums and is 16% for average stocks between these limits.
Assuming that demand is constant, what should be the re-order quantity that minimizes the total cost and what will be the corresponding annual cost, given that only full drums are supplied?