What is theJordin​ Henry's machine shop uses

2 comma 5502,550

brackets during the course of a year. These brackets are purchased from a supplier

9090

miles away. The following information is known about the​ brackets:

Annual demand

2 comma 5502,550

Holding cost per bracket per year

$ 1.35$1.35

Order cost per order

$ 18.25$18.25

Lead time

22 days

Working days per year

250250

Part 2

​a)

What is the​ EOQ?

262.55262.55

units ​(round *your response to two decimal*​ places).

Part 3

​b)

What is the average inventory if the EOQ is​ used?

131.28131.28

units ​(round *your response to two decimal*​ places).

What would be the annual inventory holding​ cost?

​$177.23177.23

​(round *your response to two decimal*​ places).

Part 4

​c)

Given the​ EOQ, how many orders will be made​ annually?

9.729.72

orders ​(round *your response to two decimal*​ places).

What would be the annual order​ cost?

​$177.39177.39

​(round *your response to two decimal*​ places).

Part 5

​d)

Given the​ EOQ, what is the total annual cost of managing​ (ordering and​ holding) the​ inventory?

​$355.10355.10

​(round *your response to two decimal*​ places).

Part 6

​e)

What is the time between​ orders?

25.7225.72

days ​(round *your response to two decimal*​ places).

Part 7

​f)

What is the reorder point​ (ROP)?

enter your response here

units ​(round *your response to two decimal*​ places).

Let's go through each part of the problem step by step. I'll break down the EOQ, average inventory, and related calculations as requested.

### Part 2: Economic Order Quantity (EOQ)
The EOQ formula is:
\[
EOQ = \sqrt{\frac{{2DS}}{H}}
\]
Where:
- $ D = \text{{Annual demand}} = 2550 $ units
- $ S = \text{{Order cost per order}} = 18.25 $ dollars
- $ H = \text{{Holding cost per unit per year}} = 1.35 $ dollars

The EOQ is given as 262.55 units (rounded to two decimal places). This is the optimal order quantity.

### Part 3: Average Inventory and Holding Cost
- **Average Inventory**: When the EOQ is used, the average inventory is simply half of the EOQ:
\[
\text{{Average Inventory}} = \frac{{EOQ}}{2} = \frac{262.55}{2} = 131.28 \text{{ units}}
\]
- **Annual Inventory Holding Cost**: This is calculated by multiplying the average inventory by the holding cost per unit:
\[
\text{{Annual Holding Cost}} = \text{{Average Inventory}} \times H = 131.28 \times 1.35 = 177.23 \text{{ dollars}}
\]

### Part 4: Number of Orders and Annual Ordering Cost
- **Number of Orders Annually**: The number of orders per year is the annual demand divided by the EOQ:
\[
\text{{Number of Orders}} = \frac{{D}}{EOQ} = \frac{2550}{262.55} = 9.72 \text{{ orders}}
\]
- **Annual Ordering Cost**: This is calculated by multiplying the number of orders by the cost per order:
\[
\text{{Annual Ordering Cost}} = \text{{Number of Orders}} \times S = 9.72 \times 18.25 = 177.39 \text{{ dollars}}
\]

### Part 5: Total Annual Cost of Managing Inventory
The total annual cost of managing the inventory is the sum of the annual holding cost and the annual ordering cost:
\[
\text{{Total Annual Cost}} = \text{{Annual Holding Cost}} + \text{{Annual Ordering Cost}} = 177.23 + 177.39 = 355.10 \text{{ dollars}}
\]

### Part 6: Time Between Orders
The time between orders can be found by dividing the number of working days per year by the number of orders:
\[
\text{{Time Between Orders}} = \frac{{\text{{Working Days per Year}}}}{\text{{Number of Orders}}} = \frac{250}{9.72} = 25.72 \text{{ days}}
\]

### Part 7: Reorder Point (ROP)
The Reorder Point is calculated based on the lead time and daily demand. First, we calculate daily demand:
\[
\text{{Daily Demand}} = \frac{D}{\text{{Working Days per Year}}} = \frac{2550}{250} = 10.2 \text{{ units/day}}
\]
Then, multiply by the lead time (22 days):
\[
\text{{ROP}} = \text{{Daily Demand}} \times \text{{Lead Time}} = 10.2 \times 22 = 224.4 \text{{ units}}
\]

### Summary
- **EOQ**: 262.55 units
- **Average Inventory**: 131.28 units
- **Annual Holding Cost**: $177.23
- **Number of Orders per Year**: 9.72 orders
- **Annual Ordering Cost**: $177.39
- **Total Annual Cost**: $355.10
- **Time Between Orders**: 25.72 days
- **Reorder Point (ROP)**: 224.4 units

Would you like further details on any of these calculations or how they relate to inventory management?

### 5 Related Questions:
1. How does an increase in holding cost affect the EOQ?
2. What happens to the total annual cost if the order cost decreases?
3. How would reducing lead time impact the reorder point?
4. What would be the impact of higher demand on the EOQ and average inventory?
5. How would extending the number of working days per year affect time between orders?

### Tip:
To minimize total inventory costs, focus on both reducing order costs and optimizing order frequency based on demand and holding costs.

Explore how to calculate Economic Order Quantity (EOQ), average inventory, holding costs, and more with a step-by-step solution. This problem involves practical inventory management calculations based on demand, order costs, and holding costs.

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