Question

The catering manager of LaVista​ 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 pieces or​ less) her vendor quotes a price of ​$1.80​/piece.

> If she orders 2,001 to 5, 000 ​pieces, the price drops to ​$1.60​/piece.

>5,001 to 10,000 pieces brings the price to ​$1.40​/piece, and

>10,001 and above reduces the price to ​$1.25​/piece.

​Lisa's order costs are ​$205 per​ order, her annual holding costs are 5​%, and the annual demand is 47,800 pieces. For the best option​ (the best option is the price level that results in an EOQ within the acceptable​ range):

​a) What is the optimum ordering​ quantity? nothing units ​(round your response to the nearest whole​ number).

​b) What is the annual holding​ cost?

​c) What is the annual ordering​ cost?

d) What are the annual costs of the silverware itself with an optimal order​ quantity?

​e) What is the total annual​ cost, including​ ordering, holding, and purchasing the​ silverware?

Answer 1

Yearly demand = 47,800 Units

Ordering cost = $205

Average Cost of one unit = (1.80 + 1.60 + 1.40 + 1.25) / 4 = $1.51

Holding cost = 5% of $1.51 per unit per year

= $0.0755

A) Optimal Order quantity = EOQ = Sq. Root [(2 x Annual demand x Ordering cost) / Holding cost]

= Sq. Root [(2 x 47800 x 205) / 0.0755]

= 16111 Units (Approx)

Hence, the Price for each unit will be $1.25 per unit

B) Average annual inventory = 16111 / 2 = 8056 Units (Approx.)

Annual Holding cost = Average annual inventory x Holding cost per unit per year

= 8056 x 0.0755

= $608.23

C) Number of orders per year = Annual demand / EOQ

= 47800 / 16111

= 2.96 Orders (Approx.)

Annual Ordering cost = No of orders per year x Per order cost

= 2.96 x 205 = $606.80

D) Total cost of purchasing = Annual demand x price per unit

= 47800 x 1.25

= $59750

E) Total Annual cost = Total cost of purchasing + Annual holding cost + Annual ordering cost

= 59750 + 606.80 + 608.23

= $60965