Question

Elizabeth Kennedy sells beauty supplies. Her annual demand for a particular skin spackle is 17,000 units. The cost of placing an order is $50, while the holding cost per unit per year is 20 percent of the cost. This item currently costs $12.50 if the order quantity is less than 1500. For orders of 1501 units up to 10,000 units the cost falls to $12.45 and for orders of 10,001 or greater, the cost falls to $12.40. To minimize total cost, how many units should Elizabeth order each time she places an order? What is the minimum total cost?

Answer 1

	Number of Orders
	<1500	1501	O>10001
Annual Demand	17000	17000	17000
Set up Cost	50	50	50
Product Cost	12.50	12.45	12.40
Holding Cost ( % of PC)	20%	20%	20%
Holding Cost( in $)	2.50	2.49	2.48
EOQ	825
Total Cost at Different Order levels	825	1500	10001
Inventory Carrying Cost	1031.25	1875	12451.245
Ste up Cost Carrying Cost	1030	567	85
Product Cost	212500	212500	211650
Total Cost	214562	214942	224186

	Number of Orders
	<1500	1501	O>10001
Annual Demand	17000	17000	17000
Set up Cost	50	50	50
Prodcut Cost	12.5	12.45	12.4
Holding Cost ( % of PC)	0.2	0.2	0.2
Holding Cost( in $)	=SUMPRODUCT(B6,B5)	=SUMPRODUCT(C6,C5)	=SUMPRODUCT(D6,D5)
EOQ	=SQRT(2*B3*B4/B7)
Total Cost at Different Order levels	825	1500	10001
Inventory Carrying Cost	=B12/2*B7	=C12/2 *B7	=D12/2 *C7
Ste up Cost Carrying Cost	=B3/B12*B4	=B3/C12*B4	=C3/D12*C4
Product Cost	=B5*B3	=B5*B3	=C5*C3
Total Cost	=SUM(B14:B16)	=SUM(C14:C16)	=SUM(D14:D16)

Formula Sheet :-

So, the Elizabeth should order 825 units each time to minimize her costs, her total costs are 214562 in this case. Including product cost)

Also,

Total Cost at Different Order levels	825	1500	10001
Inventory Carrying Cost	1031	1875	12451
Ste up Cost Carrying Cost	1030	567	85
Total cost	2062	2442	12536