Question

1.

A fresh produce distributor uses 770 non-returnable packing crates a month, which it purchases at a cost of $6 each. The manager has assigned an annual holding cost of 28 percent of the purchase price per crate. Ordering cost is $32 per order. Currently the manager orders 770 crates at a time. How much could the firm save annually in ordering and holding costs by using the EOQ? (Round the final answer to 2 decimal places.)

Annual savings A large law firm uses an average of 5 packages of copier paper a day. Each package contains 500 sheets. The firm operates 230 days a year. Holding cost for the paper is $1 per year per package, and ordering cost is $12 per order. 2. a. What order quantity would minimize total annual ordering and holding cost? (Round the final answer to the nearest whole number.)      EOQ packages      b. Calculate the total annual inventory control cost using your order quantity from part a. (Round the final answer to 2 decimal places.)      TC $       c. Except for rounding, are annual ordering and holding costs equal at the EOQ? Yes No    d. The office manager is currently using an order quantity of 160 packages. The partners of the firm expect the office to be managed in a cost-efficient manner. Would you recommend that the office manager use the optimal order quantity instead of 160 packages? Yes No

$

Answer 1

Please find below Answer to question 1 :

Following are the relevant data :

Annual demand of crates = D = 770 / MONTH X 12 MONTHS = 9240 CRATES

Ordering cost = Co = $32

Annual unit holding cost = Ch = 28 percent of $ 6 = 0.28 x 6 = $1.68

Therefore ,

Economic Order quantity ( EOQ )

= Square root ( 2 x Co x D / Ch )

= Square root ( 2 x 32 x 9240 /1.68 )

= 593.29 ( 593 crates rounded to nearest whole number )

At order quantity = 593 crates :

Annual ordering cost

= Ordering cost x Number of orders

= Ordering cost x Annual demand/ Order quantity

= Co x D/ EOQ

= $32 x 9240 / 593

=$498.62

Annual inventory holding cost

= Annual unit inventory holding cost x Average inventory

= Ch x EOQ/ 2

= $1.68 x 593/ 2

= $498.12

Therefore .

Total annual ordering plus inventory holding cost = $498.62 + $498.12 = $996.74

At order quantity = 770 crates:

Annual ordering cost

= Ordering cost x Number of orders

= Ordering cost x Annual demand/ Order quantity

= Co x D/ order quantity

= $32 x 9240 / 770

=$384

Annual inventory holding cost

= Annual unit inventory holding cost x Average inventory

= Ch x Order quantity / 2

= $1.68 x 770/2

= $ 646.80

Therefore .

Total annual ordering plus inventory holding cost = $384 + $646.80 = $1030.80

Therefore amount the firm saves annually in ordering and inventory holding cost

= $1030.80 - $996.74

= $34.06