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The problem you're facing is a typical economic order quantity (EOQ) problem that requires calculating the optimal number of engines Harley should transport to minimize costs, as well as the cycle inventory. Here's a breakdown of the problem:

### Given Data:
- **Cost per trip:** $1000
- **Motorcycle production/sales rate:** 300 motorcycles per day
- **Cost per engine:** $500
- **Annual holding cost rate:** 20% of the engine cost per year
- **Daily demand (D):** 300 engines/day

We need to find:
1. **The optimal number of engines to transport (Q)** for each trip.
2. **The cycle inventory of engines.**

### Step 1: Calculate the Annual Demand (D)
Since Harley produces 300 motorcycles per day and there are 365 days in a year:
\[
D = 300 \times 365 = 109,500 \text{ engines/year}
\]

### Step 2: Holding Cost per Engine
The holding cost is 20% of the cost of one engine, which is $500. Therefore:
\[
\text{Holding Cost per engine per year} = 0.2 \times 500 = 100 \text{ dollars/year}
\]

### Step 3: Economic Order Quantity (EOQ) Formula
The EOQ formula is used to minimize the total cost (ordering cost + holding cost). The formula is given by:
\[
Q = \sqrt{\frac{2DS}{H}}
\]
Where:
- $ Q $ = optimal order quantity (number of engines per truck)
- $ D $ = annual demand (109,500 engines/year)
- $ S $ = cost per order (or trip) = $1000
- $ H $ = holding cost per unit per year = $100

Substituting the values:
\[
Q = \sqrt{\frac{2 \times 109,500 \times 1000}{100}} = \sqrt{2,190,000} = 1,479.31
\]

Thus, Harley should transport approximately **1,479 engines** per truck.

### Step 4: Cycle Inventory
The cycle inventory is simply half of the order quantity (because inventory fluctuates between 0 and $Q$):
\[
\text{Cycle Inventory} = \frac{Q}{2} = \frac{1,479}{2} = 739.66
\]
So, the cycle inventory is approximately **740 engines**.

---

### Summary:
- **Optimal number of engines to transport per truck:** 1,479 engines
- **Cycle inventory of engines at Harley:** 740 engines

Do you need more details on this or have any questions?

---

Here are five relative questions to deepen your understanding:
1. How would changing the holding cost percentage affect the optimal order quantity?
2. What impact would an increase in the cost per trip have on the EOQ?
3. How does the EOQ model help companies like Harley Davidson minimize costs?
4. Can EOQ be applied to services, or is it strictly for inventory management?
5. What are the potential drawbacks of using EOQ in real-world logistics?

**Tip:** Always ensure that the demand rate, holding cost, and ordering cost are accurate for EOQ to give optimal results.

Harley Davidson transports engines between two plants using trucks, 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?

Learn how to calculate the Economic Order Quantity (EOQ) and cycle inventory for Harley Davidson's engine transportation system. This problem involves minimizing total costs by determining the optimal number of engines per truckload, using EOQ and inventory management formulas.

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