Question

Nick's Camera Shop carries Zodiac instant print film. The film normally costs Nick $10 per roll. Nick's average sales are 200 rolls per week. His annual inventory holding cost rate is 25% and it costs Nick $20 to place an order with Zodiac. If Zodiac offers a $1 discount on orders of 400 rolls or more and a $2 discount for 900 rolls or more, determine Nick's optimal order quantity.

Answer 1

Answer: Check for EOQ

demand per week		200	200	200
weeks per year=		52	52	52
Annual demand, D=	demand per week*weeks per year	10400	10400	10400
Order cost or setup cost, S		$20.00	$20.00	$20.00
item cost		$10.00	$9.00	$8.00
holding cost percent		25%	25.0%	25.0%
holding cost per year, H=	holding cost percent*item cost	$2.50	$2.25	$2.00
Order quantity, Q=	squareroot(2*S*D/H)	407.92	430	456

order quantity of 430 is matching the price requirement of 400 to 900 units

Now, as the EOQ is 430 units, Check total cost for Q= 399, 430 and 900 units

Annual demand, D=		10400	10400	10400
Order cost or setup cost, S		$20.00	$20.00	$20.00
item cost		$10.00	$9.00	$8.00
holding cost percent		25%	25.0%	25.0%
holding cost per year, H=	holding cost percent*item cost	$2.50	$2.25	$2.00
Order quantity, Q=		399.00	430	900
annual holding cost=	Q*H/2	$498.75	$483.74	$900.00
Annual ordering cost=	D*S/Q	$521.30	$483.74	$231.11
Purchasing cost=	annual demand*item cost	$104,000	$93,600	$83,200
Total cost=	holding cost+order cost+purchase cost	$105,020.05	$94,567	$84,331.11

the total cost of order quantity of 900 units is least. hence, 900 is Nick's optimal order quantity