Question

Item X is a standard item stocked in a company's inventory of component parts. Each year the firm, on a random basis, use about 2,00 of item X, which cost $25 each. Storage cost, which included insurance and cost of capital, amount to $5 per unit average inventory. Every time an order is placed for more of item X it cost $10.

Whenever item X is ordered, what should the order size be?
What is the annual cost for ordering item ?

Answer 1

The order size for item X should be 200 units to minimize costs. The annual cost for ordering item X is $900.

Step-by-step explanation:

To determine the order size for item X, we need to consider the economic order quantity (EOQ) formula. EOQ is calculated as the square root of (2DS/H),

where D is the annual demand, S is the ordering cost per order, and H is the holding cost per unit per year.

In this case, the annual demand is 2,000 units, the ordering cost is $10, and the holding cost is $5 per unit. Plugging in these values, we have EOQ = √(2 * 2,000 * 10 / 5)

= 200 units.

Therefore, the order size for item X should be 200 units to minimize costs.

The annual cost for ordering item X can be calculated using the EOQ formula:

Annual cost = D/Q * S + Q/2 * H,

where D is the annual demand, Q is the order size, S is the ordering cost per order, and H is the holding cost per unit per year.

Plugging in the values,

we have Annual cost = 2,000/200 * 10 + 200/2 * 5

= $400 + $500

= $900.