This problem is related to determining the Economic Order Quantity (EOQ), which minimizes the total inventory costs, including ordering and holding costs. The EOQ formula is given by:

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

Where:

• $D$ = Annual demand (in units)
• $S$ = Cost per order
• $H$ = Holding cost per unit per year

Let's break this problem into parts and calculate each necessary component.

1. Given Data

• Daily demand = 160 bags/day
• Days per year = 360 days
• Annual demand (D) = $160 \times 360 = 57,600$ bags/year
• Order cost (S) = $70
• Carrying charge (holding cost rate) = 5% of the item cost
• Cost per bag = $70
• Holding cost per unit per year (H) = $70 \times 0.05 = 3.5$ dollars per year

2. EOQ Calculation

Now, we can calculate the EOQ using the formula:

$EOQ = \sqrt{\frac{2 \times 57,600 \times 70}{3.5}}$

$EOQ = \sqrt{\frac{8,064,000}{3.5}} = \sqrt{2,304,000} \approx 1,518 \text{ units}$

3. Time Between Orders

To find how many days there are between orders, we use the following formula:

$\text{Time Between Orders} = \frac{EOQ}{\text{Daily Demand}} = \frac{1,518}{160} \approx 9.49 \text{ days}$

Final Answers

• The order quantity that minimizes inventory-associated costs is 1,518 units.
• The number of days between orders is approximately 9.49 days.

Would you like further details or have any questions?

5 Related Questions

1. What happens if the cost of placing an order increases? How does it affect EOQ?
2. How would a higher carrying charge impact the EOQ and the total cost?
3. What is the total cost of ordering and holding inventory for the calculated EOQ?
4. How would changes in daily demand affect the time between orders?
5. If the company decided to operate for 365 days instead of 360, how would this change the EOQ?

Tip:

To minimize costs effectively, regularly review both holding and ordering costs as they fluctuate over time due to market conditions or internal changes.