The catering manager of LaVista? Hotel, Lisa? Ferguson, is disturbed by the amou
ID: 330879 • 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. follows?For a small order ?(2,000 pieces or? less) her vendor quotes a price of ?$1.80/piece. follows?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 follows?10,001 and above reduces the price to ?$1.25/piece. ?Lisa's order costs are ?$195 per? order, her annual holding costs are 55?%, and the annual demand is 48,200 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 silver itself with an optimal order quality? E) what is the total annual cost including ordering, holding and purchasing?
Explanation / Answer
To be calculated:
(a) Economic order quantity (EOQ) or Optimal order quantity
(b) Annual holding cost
(c) Annual ordering cost
(d) Annual costs of silver (Purchase cost)
(e) Total annual cost
Given values:
Annual demand, D = 48,200 pieces
Ordering cost, Co = $195
Holding cost, H = 55% of purchase price
Purchase price:
(Q = < 2000 pieces), P = $1.80 per piece, Holding cost, H1 = 55% of $1.80 = $0.99
(Q = 2001 to 5000 pieces), P = $1.60 per piece, H2 = 55% of $1.60 = $0.88
(Q = 5001 to 10000 pieces), P = $1.40 per piece, H3 = 55% of $1.40 = $0.77
(Q > = 10001 pieces), P = $1.25 per piece, H4 = 55% of $1.25 = $0.69
Solution:
(a) Economic order quantity or optimal order quantity is calculated as;
EOQ = SQRT (2*D*Co) / H
where,
D = Annual demand
Co = Ordering costs
H = Holding costs
For H1 = $0.99 (Q = < 2000 pieces), P = $1.80 per piece
EOQ = SQRT (2*D*Co) / H1
EOQ = SQRT (2 x 48200 x 195) / 0.99
EOQ = 4,357.51 or 4,358 (rounding off to nearest whole number)
EOQ-1 = 4,358 units
For H2 = $0.88 (Q = 2001 to 5000 pieces), P = $1.60 per piece
EOQ = SQRT (2*D*Co) / H2
EOQ = SQRT (2 x 48200 x 195) / 0.88
EOQ = 4,621.84 or 4,622 (rounding off to nearest whole number)
EOQ-2 = 4,622 units
For H3 = $0.77 (Q = 5001 to 10000 pieces), P = $1.40 per piece
EOQ = SQRT (2*D*Co) / H3
EOQ = SQRT (2 x 48200 x 195) / 0.77
EOQ = 4,940.95 or 4,941 (rounding off to nearest whole number)
EOQ-3 = 4,941 units
For H4 = $0.69 (Q > = 10001 pieces), P = $1.25 per piece
EOQ = SQRT (2*D*Co) / H4
EOQ = SQRT (2 x 48200 x 195) / 0.69
EOQ = 5,219.53 or 5,220 (rounding off to nearest whole number)
EOQ-4 = 5,220 units
Of the above four economic order quantities, only EOQ-2 = 4,622 units (for holding cost = $0.88, P = $1.60 per piece) lies in the acceptable range of (Q = 2,001 to 5,000 pieces). Therefore,
Optimal order quantity = 4,622 units
(b) Annual holding cost is calculated as;
Annual holding cost = (EOQ/2) x H
Annual holding cost = (4622/2) x 0.88
Annual holding cost = $2,034
(c) Annual ordering cost is calculated as;
Annual ordering cost = (Annual Demand/EOQ) x Co
Annual ordering cost = (48200/4622) x 195
Annual ordering cost = $2,034
(d) Annual costs of silver (Purchase cost) is calculated as;
Annual costs of silver (Purchase cost) = Price x Annual demand
Annual costs of silver (Purchase cost) = $1.60 per piece x 48200
Annual costs of silver (Purchase cost) = $77,120
(e) Total annual cost is calculated as;
Total annual cost = Annual holding cost + Annual ordering cost + Annual costs of silver
Total annual cost = $2,034 + $2,034 + $77,120
Total annual cost = $81,188
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