The catering manager of La Vista Hotel, Lisa Ferguson, is disturbed by the amount of silverware she is losing every week. Last Friday night, when her crew tried to set up for a banquet for 500 people, they did not have enough knives. She decides she needs to order some more silverware, but wants to take advantage of any quantity discounts her vendor will offer. For a small order (2,000 or fewer pieces), her vendor quotes a price of $1.80/piece. If she orders 2,001–5,000 pieces, the price drops to $1.60/piece. 5,001–10,000 pieces brings the price to $1.40/piece, and 10,001 and above reduces the price to $1.25. Lisa’s order costs are $200 per order, her annual holding costs are 5%, and the monthly demand is 3750 pieces. For the best option:

economic order = 16,971 units

annual holding cost = $503.34

annual ordering cost = $530.32

total cost of silverware per year = $57,283.66

Explanation:

we must first calculate the holding costs for the different prices:

$1.80 x 5% = $0.09

$1.60 x 5% = $0.08

$1.40 x 5% = $0.07

$1.25 x 5% = $0.0625

EOQ = √[(2 x S x D) / H]

S = order cost = $200

D = annual demand = 45,000

H = holding cost = we will try all 4 options

EOQ₁ = √[(2 x 200 x 45,000) / 0.09] = 14,142.13 units

EOQ₂ = √[(2 x 200 x 45,000) / 0.08] = 15,000 units

EOQ₃ = √[(2 x 200 x 45,000) / 0.07] = 16,035.67 units

EOQ₄ = √[(2 x 200 x 45,000) / 0.0625] = 16,970.56 units

Since all EOQs are over 10,000 units, then we will definitely use the holding cost of $0.0625, price per unit $1.25, and economic order of 16,971 units.

annual holding cost = average inventory x holding cost = (16,971 / 2) x $0.0625 = $503.34

annual ordering cost = (45,000 / 16,971) x $200 = $530.32

total cost of silverware per year = (45,000 x $1.25) + $503.34 + $530.32 = $57,283.66