Calculating EOQ (Economic Order Quantity)

EOQ (Economic Order Quantity) is a formula that helps businesses calculate the optimal quantity of inventory to order for each purchase order. This calculation is important because it helps businesses avoid overstocking or understocking inventory, which can lead to lost sales or increased carrying costs.

Given the following information, we can calculate the EOQ:
- Annual demand: 2400
- Price per unit: 2.4
- Ordering cost per order: $x
- Storage cost: 2% per annum
- Interest rate: 10% per annum
- Lead time: half a month (or 0.5 months)

Step 1: Calculate annual ordering cost
- Annual ordering cost = [(annual demand) / EOQ] x (ordering cost per order)
- We don't know EOQ yet, but we can still calculate the annual ordering cost using a guess value for EOQ. Let's use 500 as a guess for now.
- Annual ordering cost = (2400 / 500) x x
- Annual ordering cost = 4.8x

Step 2: Calculate annual carrying cost
- Annual carrying cost = (EOQ / 2) x (storage cost per unit) x (interest rate)
- Annual carrying cost = (500 / 2) x (2% x 2.4) x 10%
- Annual carrying cost = 12

Step 3: Calculate total annual cost
- Total annual cost = annual ordering cost + annual carrying cost
- Total annual cost = 4.8x + 12

Step 4: Find optimal EOQ
- To find the optimal EOQ, we need to find the point where total annual cost is minimized. We can do this by taking the derivative of the total annual cost equation and setting it equal to 0.
- d/dEOQ (4.8x + 12) = 0
- -4.8x / (EOQ^2) = 0
- EOQ^2 = (4.8x) / 0
- EOQ = sqrt[(4.8x) / 0]
- EOQ = sqrt[(4.8x) / (2% x 2.4 x 10%)]
- EOQ = sqrt[(4.8x) / 0.0048]
- EOQ = sqrt(1000x)

Therefore, the EOQ is sqrt(1000x).