Question

Office Depot orders reams of paper. They sell approximately 15,000 reams per year. The shipping cost for a ream of paper is $2 and the holding cost is 25% of the purchase price. Given the prices below, determine the optimal order quantity and total cost of this solution.

Reams of Paper Price Per Ream

0-199 $4.50

200-499 $4.00

500 or More $3.50

Draw a graph of this data.

Answer 1

Annual Demand D = 15000 per year

Ordering Cost S = 2

Holding Cost = 25%*P

We will have to find the EOQ for all three price and quantity range -

From Price = 4.50

Holding Cost H = 25%*4.50 = 1.125

EOQ = (2DS/H)^(1/2)

EOQ = (2*15000*2/1.125)^(1/2)

EOQ = 230.94 = 231

Since 231 is out of 0-199 quantity range, hence It will not be the optimal range.

From Price = 4.00

Holding Cost = 1

EOQ = (2*15000*2/1)^(1/2)

EOQ = 244.95 = 245 reams

Quantity 245 lies well within quantity range 200-499. Hence, it will be feasible quantity. Now, we will check the cost with EOQ quantity and with order quantity 500. We will select the order quantity will least cost.

Cost at EOQ = (D/Q)*S + (Q/2)*H + D*P

Cost at EOQ = (15000/245)*2 + (245/2)*1 + 15000*4

Cost at EOQ = 60244.95

Cost with Order Quantity 500 = (15000/500)*2 + (500/2)*3.50*25% + 15000*3.50 = 52778.75

Since cost with the order quantity 500 is less than EOQ.

Hence,

Optimal Order Quantity = 500

Cost = 52778.75