Due to long standing relationship with your firm, the supplier has agreed to giv

Question

Due to long standing relationship with your firm, the supplier has agreed to give you quantity discounts based on the number of units you procure from them. The ordering cost of the product is $4000 per order. The inventory carrying cost is $25 per unit per year. The annual demand for the product is estimated as 100,000 units.

The quantity discounts are 1 to 6000 units are $1500 per unit, 6001+ units are $1200 per unit.

Will you take advantage of the price discount and order 6001 units each time? Select one: a. Yes b. No

Explanation / Answer

Due to different rates for different ordering quantities, we need to compare inventory cost for quantities at various levels.

First lets calculate EOQ for quantity < 6000 :

EOQ = (2 * Annual Demand * Cost per order)/ (Holding cost)

EOQ = (2 * 100,000 * 4000)/ 25 = 5656.85 5657 units

Hence, we see that according to this calculations, the EOQ is 6001 units.

This is also logically sound as this is the least amount we need to order to qualify for most discount and any additional quantity in an order would only increase holding costs and total inventory cost.

Answer is a. Yes

Order Quantity (q) 5657 6001 No. of Orders (O=100,000/q) 17.67 16.66 OC = Ordering Cost (O*4000) 70680 66640 HC = Holding Cost (25*q/2) 70712.5 75012.5 CP = Cost of Purchase (RespectivePrice*100,000) 150,000,000 120,000,000 TOTAL INVENTORY COST (OC+HC+CP) 150,141,392.5 120,141,652.5

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