Reference no: EM131564150

Question: INVENTORY CONTROL AND PLANNING A company expects to sell D units of a certain product per year. Sales are assumed to be at a steady rate with no shortages allowed. Each time an order for the product is placed, an ordering cost of K dollars is incurred. Each item costs p dollars, and the holding cost is h dollars per item per year.

a. Show that the inventory cost (the combined ordering cost, purchasing cost, and holding cost) is

c(x) = (KD/x) + pD + (hx/2)          (x > 0)

Where x is the order quantity (the number of items in each order) .

b. Use the result of part (a) to show that the inventory cost is minimized if

x = √(2KD/h)

This quantity is called the economic order quantity (EOQ).