Question

A food processing company uses 25,000 kg of corn flour every year. The quantity - discount price of corn flour is provided in the table below.

Quantity (kg)	Unit Price (Rs/kg)
1 - 749	70
750 - 1499	65
1500 and above	60

The order processing charges are Rs. 500/ order. The handling plus carry-over charge on an annual basis is 20% of the purchase price of the corn flour per kg. The optimal order quantity (in kg) is

• A. 1500

Answer 1

The correct option is A 1500
$\text{Annual demand, D = 25000 kg,}$

$\text{Ordering cost,}{C}_o=Rs.500\text{/order}$

Carrying cost or holding cost,

$C_h=\text{20\% of unit surface price.}$

In order to get EOQ, start checking from the lowest price.

1st case:

$EOQ,Q^{\ast }=\sqrt{\frac{2D{C}_o}{C_h}}=\sqrt{\frac{2\times 25000\times 500}{\frac{20}{100}\times 60}}$

$\text{= 1443.376 kg (not feasible)}$

II case:

$EOQ,Q^{\ast }=\sqrt{\frac{2D{C}_o}{C_h}}=\sqrt{\frac{2\times 25000\times 500}{\frac{20}{100}\times 65}}$

$\text{= 1386.75 kg (feasible)}$

$\text{Total annual cost}=DC+\sqrt{2D{C}_o{C}_h}$

$=65\times 25000+\sqrt{2\times 25000\times 500\times 0.2\times 65}$

$=162500+18027.76=Rs.1643027.76$

$\text{For 1500 kg,}$

$\text{Annual cost}=DC+\frac{D}{Q}{c}_0+\frac{C_h}{2}Q$

$=25000\times 60+\frac{1500\times 20\times 60}{2\times 100}+\frac{25000}{1500}\times 500$

$=Rs.1517320.51$

$\text{So, at 1500 kg purchase, cost is minimum then}$

$\text{EOQ = 1500 kg}$