Each​ day, a company uses 160 bags of industrial cleaner. The bags can be shipped to the company each day at a rate of 285. The cost of placing an order is ​$70​, and the carrying charge is 5​% of the​ item's ​$70 cost. The company operates 360 days per year. Calculate the order quantity that minimizes the​ company's inventory-associated costs. How many days are there between orders for the order quantity you​ calculated?
Part 2
The order quantity that minimizes the​ company's inventory associated costs is 
  
enter your response here units. ​(Enter your response rounded to the nearest whole​ number.) 


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.

Each day, a company uses 160 bags of industrial cleaner. The bags can be shipped to the company each day at a rate of 285. The cost of placing an order is $70, and the carrying charge is 5% of the item’s $70 cost. The company operates 360 days per year. Calculate the order quantity that minimizes the company’s inventory-associated costs. How many days are there between orders for the order quantity you calculated?

Learn how to calculate the Economic Order Quantity (EOQ) for a company using 160 bags of industrial cleaner daily. This step-by-step solution covers key concepts in inventory management and cost optimization. Suitable for advanced high school or college-level students studying operations research or business management.

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