To determine the optimum number of orders the firm should place per year to minimize its total inventory costs, we will use the Economic Order Quantity (EOQ) formula.

The EOQ model is used to find the optimal order quantity that minimizes the total inventory costs, which include ordering costs and holding costs.

Step 1: Calculate the Holding Cost Per Unit Per Year

The holding cost per unit per year is the total cost of holding one unit in inventory, which consists of the following components:

$\text{Holding cost per unit per year} = \text{Capital} + \text{Storage} + \text{Obsolescence} + \text{Insurance and tax}$ $\text{Holding cost per unit per year} = 1.20 + 0.80 + 0.40 + 0.60 = 3.00$

So, the holding cost per unit per year is $3.00.

Step 2: Use the EOQ Formula

The EOQ formula is:

$EOQ = \sqrt{\frac{2DS}{H}}$

Where:

• $D$ = Demand (units per year)
• $S$ = Ordering cost per order
• $H$ = Holding cost per unit per year

Given:

• $D = 5000$ units
• $S = 200$ (ordering cost per order)
• $H = 3.00$ (holding cost per unit per year)

Now, substitute these values into the EOQ formula:

$EOQ = \sqrt{\frac{2 \times 5000 \times 200}{3.00}}$

$EOQ = \sqrt{\frac{2,000,000}{3.00}}$

$EOQ = \sqrt{666,666.67} \approx 816.50$

So, the optimal order quantity (EOQ) is approximately 817 units (rounding to the nearest whole unit).

Step 3: Calculate the Optimum Number of Orders Per Year

To calculate the optimum number of orders per year, we divide the annual demand by the EOQ:

$\text{Optimum number of orders per year} = \frac{D}{EOQ}$

$\text{Optimum number of orders per year} = \frac{5000}{817} \approx 6.12$

Rounding this to the nearest whole number, the firm should place 6 orders per year.

Conclusion:

The firm should place 6 orders per year to minimize its total inventory costs.

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Would you like further details or have any questions on this? Here are some related questions for further exploration:

1. How does increasing the ordering cost impact the EOQ?
2. How does changing the holding cost per unit per year affect the optimal order quantity?
3. What is the impact of a decrease in demand on the EOQ and the number of orders per year?
4. How would fluctuations in storage or insurance costs alter the inventory strategy?
5. How does EOQ compare to other inventory models like Just-in-Time (JIT)?

Tip: The EOQ model assumes steady demand and constant lead times. In real-world scenarios, consider using a safety stock or adjusting the model for variability in demand.