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 comma 0002,000

pieces or​ less) her vendor quotes a price of

​$1.801.80​/piece.

follows≻If

she orders

2 comma 0012,001

to

5 comma 0005,000

​pieces, the price drops to

​$1.601.60​/piece.

follows≻5 comma 0015,001

to

10 comma 00010,000

pieces brings the price to

​$1.401.40​/piece,

and

follows≻10 comma 00110,001

and above reduces the price to

​$1.251.25​/piece.

​Lisa's order costs are

​$200200

per​ order, her annual holding costs are

55​%,

and the annual demand is

44 comma 90044,900

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?

units ​(round your response to the nearest whole​ number).

​b) What is the annual holding​ cost?

​$nothing

​(round your response to two decimal​ places).

Answer 1

find approximate EOQ

Annual demand, D=	demand per day*days per year	44900
Order cost or setup cost, S		$200.00
item cost		$1.80
holding cost percent		55%
holding cost per year, H=	holding cost percent*item cost	$0.99
Order quantity, Q=	squareroot(2*S*D/H)	4259

Approx EOQ= 4259

hence we will check total cost for order quantity EOQ, 5000 and 10000 ar their respective cost.

Annual demand, D=		44900	44901	44902
Order cost or setup cost, S		$200.00	$201.00	$202.00
item cost		$1.60	$1.40	$1.25
holding cost percent		55%	55%	55%
holding cost per year, H=	holding cost percent*item cost	$0.88	$0.77	$0.69
Order quantity, Q=		squareroot(2*S*D/H)= 4518	5000	10000
annual holding cost=	Q*H/2	$1,987.8	$1,925.0	$3,437.50
Annual ordering cost=	D*S/Q	$1,987.8	$1,805.0	$907
Purchasing cost=	annual demand*item cost	$71,840	$62,861	$56,128
Total cost=	holding cost+order cost+purchase cost	$75,816	$66,591	$60,472

1. the best option is the order quantity of 10,000

2. annual holding cost= $3,437.50