Let's break down the problem step by step: ### **Given Data:** - Annual demand (\(D\)) = 25,000 bags/year - Ordering cost (\(S\)) = $10/order - Holding (carrying) cost (\(H\)) = $2/bag/year - Number of working days/year = 300 - Lead time = 3 days - No backordering We are asked for the **total inventory cost at EOQ** (Economic Order Quantity). --- ### **Step 1: Calculate EOQ** The EOQ formula is: \[ EOQ = \sqrt{\frac{2DS}{H}} \] Plug in the values: \[ EOQ = \sqrt{\frac{2 \times 25,000 \times 10}{2}} \] \[ EOQ = \sqrt{\frac{500,000}{2}} \] \[ EOQ = \sqrt{250,000} \] \[ EOQ = 500 \text{ bags} \] --- ### **Step 2: Calculate the Total Inventory Cost at EOQ** Total inventory cost at EOQ = Ordering cost + Holding cost #### **A. Ordering Cost per Year** \[ \text{Number of orders/year} = \frac{D}{EOQ} = \frac{25,000}{500} = 50 \] \[ \text{Annual ordering cost} = \text{Number of orders/year} \times S = 50 \times 10 = \$500 \] #### **B. Holding Cost per Year** \[ \text{Average inventory} = \frac{EOQ}{2} = \frac{500}{2} = 250 \text{ bags} \] \[ \text{Annual holding cost} = \text{Average inventory} \times H = 250 \times 2 = \$500 \] --- ### **Step 3: Add the Costs** \[ \text{Total annual inventory cost at EOQ} = \$500 (\text{ordering}) + \$500 (\text{holding}) = \$1,000 \] --- ## **Final Answer** \[ \boxed{1000} \]

The total inventory cost is the sum of the costs for ordering and holding inventory annually. Calculating the EOQ minimizes these combined costs, resulting in the lowest total inventory expense.