C_h = ₹ 0.50 unit/month

C_o = ₹ 550/order

D = 10000 units/yr

Demand is fixed & shortage cost is infinity

Using classical EOQ, the optimal lot size _______ units/order (nearest integer)

The correct answer is 1354.

To find the optimal lot size (Economic Order Quantity, EOQ), we use the classical EOQ formula. Let us first list the given data and convert all values to a consistent time unit (yearly basis):

Annual Demand (D) = 10,000 units/year
Ordering Cost (C_o) = ₹ 550/order
Holding Cost (C_h) = ₹ 0.50/unit/month

Since the demand is given on an annual basis, we must convert the holding cost to an annual holding cost per unit. Since there are 12 months in a year:

$$C_h=0.50\times 12=6\text{ per unit/year}$$

The classical EOQ formula for the optimal lot size (Q^*) is given by:

$$Q^{*}=\sqrt{\frac{2\times D\times C_o}{C_h}}$$

Substituting the values into the formula:

$$Q^{*}=\sqrt{\frac{2\times 10000\times 550}{6}}$$

Simplifying the expression inside the square root:

$$Q^{*}=\sqrt{\frac{11000000}{6}}$$

$$Q^{*}=\sqrt{1833333.33}$$

Calculating the square root:

$$Q^{*}\approx 1354.006$$

Rounding to the nearest integer, we get the optimal lot size as 1354 units/order.