Question

Problem 11-21 Item X is a standard item stocked in a company's inventory of component parts. Each year the firm, on a random basis, uses about 1,700 of item X, which costs $25 each. Storage costs, which include insurance and cost of capital, amount to $4 per unit of average inventory. Every time an order is placed for more item X, it costs $22. a. Whenever item X is ordered, what should the order size be? (Round your answer to the nearest whole number.) Order size b. What is the annual cost for ordering item X? (Round your answer to 2 decimal places.) Ordering cost $ c. What is the annual cost for storing item X? (Round your answer to 2 decimal places.) Holding cost $

Answer 1

Answer:

a) the order size of item X should be 137 units

b) the annual ordering cost for item X is $ 272.99

c) the annual holding cost for item X is $ 274

Explanation:  

Given the data in the question;

a) Whenever item X is ordered, what should the order size be?

The Economic Order quality EOQ is the optimum quantity that should normally be ordered, its is expressed as;

$Q_{opt$ = √( 2DS/H)

where D is the annual demand, S is set up cost and H is the holding cost.

given that; the annual demand is 1700 units and the holding cost is $4 per unit per year, cost of placing order is $22.

So, we use the Economic Order quality EOQ;

$Q_{opt$ = √( 2DS/H)

we substitute

$Q_{opt$ = √( (2 × 1700 × 22 ) / 4)

$Q_{opt$ = √( 74800 / 4 )

$Q_{opt$ = √18700

$Q_{opt$ = 136.75 ≈ 137 units

Therefore, the order size of item X should be 137 units

b) What is the annual cost for ordering item X.

Annual ordering cost = actual number of placed orders × cost of each order

Annual ordering cost = D/Q × s

we substitute

Annual ordering cost = (1700 / 137) × 22

Annual ordering cost = 12.408759 × 22

Annual ordering cost = 272.99

Therefore, the annual ordering cost for item X is $ 272.99

c) What is the annual cost for storing item X.

Holding cost = average inventory × cost of storage per unit

Holding cost = Q/2 × H

we substitute

Holding cost = 137/2 × 4

Holding cost = 68.5 × 4

Holding cost = $ 274

Therefore, the annual holding cost for item X is $ 274