A local tyre distributor expects to sell approximately 9600 steel belted radial tyres next year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic order quantity of the tyres is

The correct option is 300.

Understanding Economic Order Quantity (EOQ):
The Economic Order Quantity (EOQ) is a model used in operations and inventory management to determine the optimal order quantity that minimizes the total inventory costs, which include ordering costs and holding (carrying) costs.

The mathematical formula to calculate EOQ is:

$$\mathrm{EOQ}=\sqrt{\frac{2·D·S}{H}}$$

Where the parameters are defined as:
• $D$ = Annual Demand = 9600 tyres
• $S$ = Ordering Cost per order = Rs. 75
• $H$ = Annual Carrying (Holding) Cost per tyre = Rs. 16

Step-by-Step Derivation:

First, calculate the product in the numerator:

$$2·D·S=2·9600·75=1440000$$

Next, divide this numerator value by the annual carrying cost ($H$):

$$\frac{1440000}{16}=90000$$

Finally, find the square root of the result to calculate the economic order quantity:

$$\mathrm{EOQ}=\sqrt{90000}=300$$

Therefore, the distributor should place orders of 300 tyres at a time to minimize total costs.