Question

A publisher workshop operates 200 days/year. The daily demand of paper is 200 rolls. The cost placing an order is $40 and the annual inventory holding cost is 20% of the unit price. Below table shows the unit prices for different quantity level the item.

Quantity	Unit Price
1-1,499	$2.50 per unit
1,500 - 2,999	$2.2 per unit
3,000 – 4,999	$2.00 per unit
5,000 or more	$1.50 per unit

What is the optimal order quantity?

What is the total cost at the optimum order quantity?

Answer 1

Annual demand = 200 days * 200 rolls = 40,000 units

ordering cost = $40

holding cost = 20% of unit price

	Optimal order quantity (EOQ)	Purchase cost	Ordering cost	Holding cost	Total cost
@$2.5	= = = 2530 units
@2.2	= = 2697 units	= 40000*$2.2 =$88,000	=(40000/2697)*40 =$593	= (2697/2)*(2.2*0.20) =$593	=$89186
@$2	= = 2829 units
@$1.5	= = 3266 units

So, as per the above calculation, at unit price of @$2.2 the optimal quantity lies between the given range of 1500-2999 units and therefore it the optimal order quantity.

And the total cost of optimal order quantity is $89,186