Question

X Ltd. Produces a product which has an annual demand of 48000 units. The product requires a component beta which is produced at Rs.20. For every finished product, one unit of the component is required. The ordering cost is Rs.120 per order and the holding cost is 10% p.a. Execute EOQ Calculation.

Answer 1

To execute the EOQ (Economic Order Quantity) calculation, we need to determine the optimal order quantity that will minimize the total cost of holding and ordering.

Given:
Annual demand (D) = 48000 units
Cost per order (S) = Rs.120
Holding cost (%) = 10%

Step 1: Calculate the annual ordering cost (AOC)
AOC = (D / Q) * S
where Q is the order quantity

Step 2: Calculate the annual holding cost (AHC)
AHC = (Q / 2) * H * P
where H is the holding cost percentage and P is the cost per unit

Step 3: Set the AOC equal to the AHC and solve for Q
(D / Q) * S = (Q / 2) * H * P

Step 4: Simplify the equation
(D * S) = (Q^2 * H * P) / 2

Step 5: Solve for Q
Q^2 = (2 * D * S) / (H * P)
Q = square root of [(2 * D * S) / (H * P)]

Now let's substitute the given values:
D = 48000 units
S = Rs.120
H = 10% = 0.1
P = Rs.20

Q = square root of [(2 * 48000 * 120) / (0.1 * 20)]
Q = square root of (11520000 / 4)
Q = square root of 2880000
Q ≈ 169.71

Therefore, the optimal order quantity (EOQ) is approximately 170 units.