Noworo wentory of them space to 4,000 c . A ton of the first item occupies 1,000 oft, and a ton of the second item 500 e. f. Find the optimal lot size [/SI, 1971) Ans 2 tons, 4 tons.) 12.7 INVENTORY MODELS WITH PRICE BREAKS In the inventory models discussed so far the production or purchase cost per unit was assumed to be constant. It was not considered during their formulation since it did not affect the level of inventory In this section we shall consider a class of inventory problems in which this cost is variable and depends upon the quantity manufactured or purchased This usually happens when discounts are offered for the purchase of large quantities. These discounts take the form of price breaks. For example, the price breaks may be given as I per item for purchase of items upto 500, 095 per item for purchase of items from 501 upto 1,000, 0.90 per item for purchase of items 1,001 or more Clearly, the purchase cost C(q) is a variable and is given by the expression 11.4 Os qs 500, C(q) = 1x 500 +0.95 (q - 500) 501 sq 5 1,000, 1 x 500 +0.95 (1.000 - 500) + 0.90 (9-1.000) 921,001 Such a variable cost must be considered in the inventory model. Further, as this variable production or purchase cost per unit is more appropriate for purchased parts (because of quantity discounts), we shall, hereafter, refer only to purchased parts and the problem, then, is to determine ( how often the parts be purchased, (1how many units should be purchased at anyone time. 12.7-1 Inventory Models with One Price Break To understand how the optimal order quantity can be determined in such a case, let us consider example 12.7-1 b20 1152 OPERATIONS RESEARCH EXAMPLE 12.7-1 An automobile manufacturer purchases 2.100 casting over a period of 360 days. This requirement is fixed and known. These castings are subject to quantity discounts. Ordering cost is 70,000 order and storage cost per day ix 0.12% of the unit cost. Determine the optimal purchase quantity of the supplier has offered the following unil prices for the castings: Unit price =1,000 for a