# Economic Order Quantity (EOQ) Problem Given: - **Annual demand (\(D\))** = 4000 units - **Ordering cost per order (\(S\))** = $200 - **Carrying cost per unit per year (\(H\))** = $5 --- ## (a) Find EOQ The EOQ formula is: \[ EOQ = \sqrt{ \frac{2DS}{H} } \] Where: - \(D\) = Annual demand - \(S\) = Ordering cost per order - \(H\) = Carrying (holding) cost per unit per year **Step 1: Substitute the values** \[ EOQ = \sqrt{ \frac{2 \times 4000 \times 200}{5} } \] **Step 2: Calculate the numerator** \[ 2 \times 4000 \times 200 = 1,600,000 \] **Step 3: Divide by carrying cost** \[ \frac{1,600,000}{5} = 320,000 \] **Step 4: Take the square root** \[ EOQ = \sqrt{320,000} \approx 565.69 \] **Final EOQ:** \[ \boxed{566 \text{ units (rounded to nearest whole unit)}} \] --- ## (b) Calculate Total Ordering Cost and Total Carrying Cost at EOQ ### 1. Total Ordering Cost \[ \text{Total Ordering Cost} = \left(\frac{D}{EOQ}\right) \times S \] \[ = \left(\frac{4000}{566}\right) \times 200 \approx 7.07 \times 200 = \$1,414 \] ### 2. Total Carrying Cost \[ \text{Total Carrying Cost} = \left(\frac{EOQ}{2}\right) \times H \] \[ = \left(\frac{566}{2}\right) \times 5 = 283 \times 5 = \$1,415 \] --- ## Summary Table | Parameter | Value | |--------------------------|--------------| | EOQ | 566 units | | Total Ordering Cost | $1,414 | | Total Carrying Cost | $1,415 | --- ## Final Summary - The **Economic Order Quantity (EOQ)** is **566 units**. - At EOQ, the **total ordering cost** is **$1,414** and the **total carrying cost** is **$1,415** per year. - At EOQ, the ordering and carrying costs are approximately equal, as expected by the EOQ model.

# Economic Order Quantity (EOQ) Problem Summary ## (a) Find EOQ 1. **Calculation Process**: The EOQ formula is used to determine the optimal order size that minimizes total inventory costs. Substituting the given values yields an EOQ of approximately 566 units after performing the necessary calculations. 2. **Final Result**: The final Economic Order Quantity is rounded to **566 units**. --- ## (b) Calculate Total Ordering Cost and Total Carrying Cost at EOQ ### 1. Total Ordering Cost 1. **Calculation Method**: The total ordering cost is calculated by determining how many orders are placed annually and multiplying this by the cost per order. For the EOQ of 566 units, the total ordering cost is approximately $1,414. 2. **Final Result**: The total ordering cost at EOQ is **$1,414**. ### 2. Total Carrying Cost 1. **Calculation Method**: The total carrying cost is derived by taking half of the EOQ and multiplying it by the carrying cost per unit. This results in a total carrying cost of approximately $1,415. 2. **Final Result**: The total carrying cost at EOQ is **$1,415**. --- ## Overall Summary - The EOQ is determined to be **566 units**, which balances ordering and carrying costs effectively. - At this EOQ, the total ordering cost is **$1,414** and the total carrying cost is **$1,415**, indicating a minimal cost scenario for inventory management.