The catering manager of LaVista? Hotel, Lisa? Ferguson, is disturbed by the amou
ID: 331892 • Letter: T
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 48,800
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?
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?
Explanation / Answer
SOLUTIONS
D (annual demand) will be 48800
S (order costs) will be $205
I will be 5% of the unit price
H will be IP
We have to first determine the best order.
Because all the solutions will give Q for all the values greater than 10,000, hence the best order shall be chosen as the price of $1.25
Optimal order quantity
Q= (2DS/IP)0.5
= [(2*48800*205) / (5%* 1.25)]0.5
= 17892.12
Annual holding cost
= (Q/2) (IP)
= (17892.12/2)(5%*1.25)
= 559.13
Annual ordering (set up) cost
= (D/Q)*(S)
= (48800/17892.12) * 205
= 559.13
Annual costs of the silverware itself with an optimal order quantity=?
??P*D= 1.25*48800
=61000
Total annual cost, including ordering, holding, and purchasing the silverware
= 559.13+559.13+61000
=62118.26
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