Question

Cavendish Convenience Stores purchases 1000 U.S. Road Maps a year for its inventory from its supplier, who offers pricing at quantity discounts. The cost for Cavendish to place an order is $42, and the annual carrying cost is 15%/year. What quantity should Cavendish order? The quantities and pricing from this supplier are shown in the following table: ORDER QUANTITY UNIT PRICE 0-149 $12.00 150-349 $11.70 350-999 $11.50 1000 or more $11.20 a) What is the EOQ when the unit price is $12? b) What is the total cost (holding + purchase+ ordering) when purchasing from the supplier where the unit price is $11.70? c) What is the total cost (holding + purchase+ ordering) when purchasing from the supplier where the unit price is $11.50? d) What is the total cost (holding + purchase+ ordering) when purchasing from the supplier where the unit price is $11.20? e) Based on the total costs, what quantity should be ordered from the supplier?

Answer 1

Please find below the response to part a -d in the table below.

Order quantity of 350 yields lowest total cost (holding + purchase+ ordering) and must be ordered.

Annual demand, D	1000
Order cost, Co	$42
Quantity	0-149	150-349	350-999	1000+
Cost, C	$12.00	$11.70	$11.50	$11.20
Holding cost , Cc	$1.80	$1.76	$1.73	$1.68
	(15%*12)	(15%*11.70)	(15%*11.50)	(15%*11.20)
EOQ = sqrt(2DCo/Cc)	216.02	218.78	220.67	223.61
Considered Order quantity - Q for calculation	149.00	218.78	350	1000
	Considered 149, max order range as EOQ is above the range	Q= 218.78 , EOQ	Consider min 350 to get a price discount as EOQ is below the range	Consider min 1000 to get a price discount
Order size	0-149	150-349	350-999	1000+
Road maps cost (Purchase)= D*Cost, Different Costs	$12,000.0	$11,700.0	$11,500.0	$11,200.0
Holding cost = (Q/2) * Cc, Differenct Q as mentioned above	$134.10	$191.98	$301.88	$840.00
Ordering cost = (D/Q) * Co	$281.88	$191.97	$120.00	$42.00
Total cost = Sum of above 3	$12,415.98	$12,083.95	$11,921.88	$12,082.00