Question

Consider the following data for an item.
Annual demand : 2500 units per year
Ordering cost : Rs. 100 per order
Inventory holding rate: 25% of unit price

Price quoted by a supplier

Order quantity (units)	Unit price (Rs.)
< 500	10
> 500	9

The optimum order quantity (in units) is

• A. 500
• B. 447
• C. $\ge 600$
• D. 471

Answer 1

The correct option is A 500

$\text{Given data:}$

$\text{Annual demand: D = 2500 units per year}$

$\text{Ordering cost:}{C}_0=\text{Rs. 100 per order}$

$\text{Inventory holding rate: i = 0.25 of units prices}$

Case 1: Let economic order quality is less than 500 for the inventory holding cost

$C_C=\frac{25}{100}\times 10=2.5$

For this case

$EOQ=\sqrt{\frac{2D{C}_0}{C_C}}$

$=\sqrt{\frac{2\times 2500\times 100}{2.5}}=447.2$

Inventory cost (TIC)

$=\sqrt{2\times C_0\times C_C\times D}$

$=\sqrt{2\times 100\times 0.25\times 10\times 2500}$

$=1118.03$

Case 2: Let EQQ is greater than 500 (EOQ . 500) for this case

$C_C=\frac{25}{100}\times 9=2.25$

$EOQ=\sqrt{\frac{2\times 2500\times 100}{2.25}}=471.4$

This is against the assumption made so correct



EOQ = 447.2 = 447 units.

When price break occurs

TIC at Q = 500

TIC = (Average inventory) × (unit inventory carrying cost) + (No. of order per year) × (cost of order)

$=\frac{Q}{2}\times C_C+\frac{D}{Q}\times C_O$

$=\frac{500}{2}\times 9\times .25+\frac{2500}{500}\times 100=1062.5$

$\text{Hence, quantity to be ordered is 500.}$