Given are the following information :

Annual demand = D = 500 / week x 50 weeks = 25000 per annum

Ordering cost for John Snow of Pet store = Co = $100 per order

Annual unit inventory holding cost = Ch = 15% of $15 per pack = $2.25 per pack

Number of packs of food should PS order at a time as per Economic Order Quantity ( EOQ ) model

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

= Square root ( 2 x 100 x 25000/2.25)

= 1490.71 ( 1491 )

PS should order 1491 PACKS AT A TIME

Total order cost for 1 year

= Ordering cost x Number of orders

= Co x Annual demand /EOQ

= $100 x 25000/1491

= $1677

Total holding cost for 1 year

= Annual unit inventory cost x Average inventory

= Ch x EOQ/ 2

= $2.25 X 1491/2

= $1677.37

Total ordering cost for 1 year = $1677

Total holding cost for 1 year = $1677.37

Average inventory in the system= EOQ/ 2 = 1491/2 = 745.5

PS’s yearly inventory turn = Annual demand/ Average inventory = 25000/ 745.5 = 33.53

Reorder level = Average weekly demand x Lead time ( weeks ) = 500 x 3 = 1500

YEARLY INVNETORY TURN = 33.53

REORDER LEVEL = 1500

At 1 percent quantity discount and order quantity of 5000 :

Revised annual unit inventory holding cost , Ch = 15% of ( 99% of $15) = $2.227

Revised annual inventory holding cost = Ch x Ordering quantity /2 = $2.227 x 5000/2 = $5567.5

Revised annual ordering cost = Co x Annual demand/Order quantity = $100 x 25000/5000 = $500

Total annual cost of inventory holding and annual ordering = $5567.5 + $500 = $6067.5

Original annual ordering plus inventory holding cost = $1677 + $1677.37 = $3354.37

Therefore , total cost of ordering plus inventory carrying for order quantity of 5000 increases by = $6067.5 – $3354.37 = $2713.13

However annual savings in cost/ unit over 25000 units annually

= 1 % discount on $15 per pack x 25000 packs

= $0.15 x 25000

= $3750

Therefore , savings in product cost ( $3750) is more than increase in ordering and inventory holding cost of $3354.37 resulting in a net savings of = $3750 – $3354.37 = $395.63

Therefore , PS should begin ordering 5000 or more packs at a time

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