Question

purchases 40,000 boxes of ice cream cones over each 200-dav dering costs are $100 7-5 The Ethel Company period of business. Carrying costs are $2 per box and or per order. The company desires to maintain a safety stock of 500 boxes (on hand initially) and two days are required for delivery (a) What is the economic order quantity? (b) What is the optimal number of orders to be placed? (c) What is the total inventory cost associated with the economic order quan-tity? (d) What is the reorder point? e) The company can obtain a quantity discount of $0.02 per box if it in- creases its order size to 3,000 boxes. Should The Ethel Company increase its order size to take the cash discount offered?

Answer 1

Solution:

a. Economic order quantity (EOQ) = √2AO/ C

Here A = annual demand or production = 40,000 boxes

O = Order cost = $100

C = Carrying costs =$2 per box

thus, EOQ = √2×40,000×$100/ $2 = 2,000 boxes

b. Optimal number of orders to be placed = 40,000/2,000= 20

C. Total inventory cost associated with EOQ = √2AOC

= √2×40,000×$100×$2 = $4,000

d. Reorder Point = (Average daily usage × Lead time ) + safety stock = {(40,000/200)×2} + 500 = 900 units

e. Evaluation of cash discount offer :

Total cost at Order size of 3,000 boxes = C + O - cash discount =(3,000/2)×$2 + (40,000/3,000)×$100 - 3,000×0.02

= 1,500 + (13orders×$100) - 60 = $4,240

The Eathel Company should not increase its order size since total cost at EOQ level is lower than it would be at new order size.