https://file.aiquickdraw.com/mathbot/file/1726416818656rgd0zzng.jpg

The text in the image is as follows:

---

**Harley Davidson transported engines between two plants using a truck, with each trip costing $1000. The motorcycle plant assembles and sells 300 motorcycles each day. Each engine costs $500, and Harley incurs a holding cost of 20% per year. How many engines should Harley load onto a truck to transport to the assembly unit? What is the cycle inventory of engines at Harley?**

---

This problem involves the Economic Order Quantity (EOQ) model for transportation and inventory management. The objective is to determine the optimal number of engines to transport in order to minimize the total transportation and holding costs.

### Let's define the parameters:
- **Trip cost** = $1000 per truckload
- **Motorcycles assembled per day** = 300 engines/day
- **Cost per engine** = $500
- **Holding cost rate** = 20% per year (0.20)
- **Annual demand for engines** = 300 engines/day × 365 days = 109,500 engines/year

### Economic Order Quantity (EOQ) formula for this situation:

\[
EOQ = \sqrt{\frac{{2DS}}{H}}
\]
Where:
- $ D $ = Annual demand for engines = 109,500 engines/year
- $ S $ = Fixed transportation cost per trip = $1000
- $ H $ = Holding cost per engine per year = 20% of $500 = $100

Substituting the values:

\[
EOQ = \sqrt{\frac{{2 \times 109,500 \times 1000}}{100}}
\]

I will now calculate the EOQ and solve for the optimal number of engines per truckload.The optimal number of engines that Harley should load onto a truck, based on the Economic Order Quantity (EOQ) model, is approximately **1,480 engines** per trip.

### Cycle Inventory:
The cycle inventory is half of the EOQ, representing the average number of engines held in inventory throughout the cycle. It is given by:

\[
\text{Cycle Inventory} = \frac{\text{EOQ}}{2} = \frac{1479.86}{2} \approx 740 \text{ engines}
\]

Thus, the average cycle inventory of engines at Harley is **740 engines**.

Would you like further details or clarifications on this? Here are some related questions:

1. How is the EOQ formula derived, and why does it minimize costs?
2. What impact does increasing the transportation cost have on EOQ?
3. How would a change in the holding cost rate affect the optimal order quantity?
4. What happens to the inventory levels if the demand for motorcycles fluctuates seasonally?
5. How can Harley balance transportation and inventory costs more efficiently?

**Tip:** EOQ helps balance holding costs and ordering costs, ensuring that neither too many nor too few units are held in inventory.

Harley Davidson transported engines between two plants using a truck, with each trip costing $1000. The motorcycle plant assembles and sells 300 motorcycles each day. Each engine costs $500, and Harley incurs a holding cost of 20% per year. How many engines should Harley load onto a truck to transport to the assembly unit? What is the cycle inventory of engines at Harley?

This problem explores how Harley Davidson can optimize engine transportation between plants using the Economic Order Quantity (EOQ) model. Learn how to calculate the optimal number of engines per truckload and the cycle inventory to minimize total transportation and holding costs. Suitable for undergraduate students studying Operations Management or Business Logistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation