Question

The following data correspond to a proposal for incremental discounts. The price of component AB is $ 0.60 each in quantities of 500 or less. For quantities between 500 and 1000, they cost $ 0.58 and for quantities of more than 1000 $ 0.56 each.

If the cost to place an order is $ 20, the annual demand is 800 units, and the cost to maintain inventory is 20%, it determines the quantity to buy.

Q ( Cantidad)	Discount %	Costo Unitario
0   - 999	0 %	5
1 000   -   1 999	2 %
2 000    o   más	3 %

Answer 1

Qty	0-500	500-1000	1000 and more
Price	0.6	0.58	0.56
Ordering Cost	20	20	20
Annual Demand	800	800	800
Inventory Holding Cost rate	20%	20%	20%
Inventory Holding Cost	0.12	0.116	0.112
Optimal Qty	516.3978	525.2257	534.5225

The optimal quantity which should be bought is the quantity minimizing the total cost.

EOQ is the quantity which minimizes the cost

EOQ = (2*annual demand*ordering cost / holding cost)

Holding cost rate = 20%

Holding cost per unit = 20% of cost price

As the price is different for different quantities, the holding costs are different.

Using the EOQ formula optimal quantity for each of the quantity options are calculated.

The optimal unit in each of the cases is greater than 500 but less than 1000.

Whether 516, 525 or 534 units are ordered, the cost applicable is that of the range 500 - 1000 but the total cost would be lowest for this range if 525 units are ordered,

Hence the optimal quantity to buy is 525.