I need help. It is due today. The answer for question b, 465 units is false/not correct The two images are the examples on how to solve the problem. 1. Petromax Enterprises uses a continuous review inventory control system for one of its SKUs. The following information is available on the item. The firm operates 52 weeks in a year. Refer to the standard normal table for z-values. ≻Demand = 78,000 units/year ≻Ordering cost = $30.00/order ≻Holding cost = $3.00/unit/year ≻Average lead time = 1 week ≻Standard deviation of weekly demand = 200 units The answer for a is: a. The economic order quantity for this item is 1249 units. (Enter your response rounded to the nearest whole number.) FIND b, please b. If Petromax wants to provide a 98% service level, the safety stock is "what?" units (enter your response rounded to the nearest whole number)
I need help. It is due today. The answer for question b, 465 units is false/not correct The two images are the examples on how to solve the problem. 1. Petromax Enterprises uses a continuous review inventory control system for one of its SKUs. The following information is available on the item. The firm operates 52 weeks in a year. Refer to the standard normal table for z-values. ≻Demand = 78,000 units/year ≻Ordering cost = $30.00/order ≻Holding cost = $3.00/unit/year ≻Average lead time = 1 week ≻Standard deviation of weekly demand = 200 units The answer for a is: a. The economic order quantity for this item is 1249 units. (Enter your response rounded to the nearest whole number.) FIND b, please b. If Petromax wants to provide a 98% service level, the safety stock is "what?" units (enter your response rounded to the nearest whole number)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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I need help. It is due today.
The answer for question b, 465 units is false/not correct
The two images are the examples on how to solve the problem.
1. Petromax Enterprises uses a continuous review inventory control system for one of its SKUs. The following information is available on the item. The firm operates 52 weeks in a year. Refer to the
standard normal table for z-values.
≻Demand = 78,000 units/year
≻Ordering cost = $30.00/order
≻Holding cost = $3.00/unit/year
≻Average lead time = 1 week
≻Standard deviation of weekly demand = 200 units
The answer for a is:
a. The economic order quantity for this item is 1249 units.
(Enter your response rounded to the nearest whole number.)
(Enter your response rounded to the nearest whole number.)
FIND b, please
b. If Petromax wants to provide a 98% service level, the safety stock is "what?" units (enter your response rounded to the nearest whole number)
![**Inventory Control System - Economic Order Quantity**
Petromax Enterprises uses a continuous review inventory control system for one of its SKUs. The following information is available on the item. The firm operates 48 weeks in a year. Refer to the standard normal table for z-values.
- **Demand** = 52,000 units/year
- **Ordering cost** = $38.00/order
- **Holding cost** = $2.50/unit/year
- **Average lead time** = 1 week
- **Standard deviation of weekly demand** = 120 units
**a. What is the economic order quantity?**
The economic order quantity (EOQ) is calculated using the formula:
\[ \text{EOQ} = \sqrt{\frac{2DS}{H}} \]
where:
- \( D \) is the demand in units per year,
- \( S \) is the ordering cost,
- \( H \) is the inventory holding cost.
For this item, the economic order quantity is:
\[ \sqrt{\frac{2 \times 52,000 \times 38.00}{2.50}} = 1,257 \text{ units} \]
This calculation helps determine the optimal order size to minimize total inventory costs, including ordering and holding expenses.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36a81628-4e73-47c6-859d-2f57e4b1f42c%2Fcc717508-0bf1-45a1-aa45-bcb241df3117%2Fewnenj_processed.png&w=3840&q=75)
Transcribed Image Text:**Inventory Control System - Economic Order Quantity**
Petromax Enterprises uses a continuous review inventory control system for one of its SKUs. The following information is available on the item. The firm operates 48 weeks in a year. Refer to the standard normal table for z-values.
- **Demand** = 52,000 units/year
- **Ordering cost** = $38.00/order
- **Holding cost** = $2.50/unit/year
- **Average lead time** = 1 week
- **Standard deviation of weekly demand** = 120 units
**a. What is the economic order quantity?**
The economic order quantity (EOQ) is calculated using the formula:
\[ \text{EOQ} = \sqrt{\frac{2DS}{H}} \]
where:
- \( D \) is the demand in units per year,
- \( S \) is the ordering cost,
- \( H \) is the inventory holding cost.
For this item, the economic order quantity is:
\[ \sqrt{\frac{2 \times 52,000 \times 38.00}{2.50}} = 1,257 \text{ units} \]
This calculation helps determine the optimal order size to minimize total inventory costs, including ordering and holding expenses.
![**Calculating Safety Stock and Reorder Point for a 96% Service Level**
To achieve a 96% service level, the safety stock and reorder point need to be determined. Here’s a step-by-step process:
**Step 1: Calculate Safety Stock**
The formula for calculating safety stock in a continuous review system is:
\[ z\sigma_{dLT}, \text{ where } \sigma_{dLT} = \sigma_d \sqrt{L}. \]
- **Given:**
- Standard deviation of weekly demand (\(\sigma_d\)) = 120 units
- Lead time (\(L\)) = 1 week
Using the standard normal table, for a 96% service level, the z-value is 1.75.
Therefore, the safety stock calculation is:
\[ 1.75 \times 120 \times \sqrt{1} = 210 \text{ units}. \]
**Step 2: Calculate Demand During Lead Time**
First, calculate weekly demand (\(\bar{d}\)):
\[ \bar{d} = \frac{\text{Demand}}{\text{Work Weeks per Year}} = \frac{52,000}{48} = 1,083 \text{ units}. \]
Now, calculate demand during lead time (\(\bar{dL}\)):
\[ \bar{dL} = 1,083 \times 1 = 1,083 \text{ units}. \]
**Step 3: Calculate Reorder Point**
The reorder point (\(\text{R}\)) is the sum of demand during lead time and safety stock:
\[ \text{R} = 1,083 + 210 = 1,293 \text{ units}. \]
This detailed process helps in determining the appropriate safety stock and reorder point to maintain a desired service level in inventory management.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36a81628-4e73-47c6-859d-2f57e4b1f42c%2Fcc717508-0bf1-45a1-aa45-bcb241df3117%2Fqk2pm0g_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculating Safety Stock and Reorder Point for a 96% Service Level**
To achieve a 96% service level, the safety stock and reorder point need to be determined. Here’s a step-by-step process:
**Step 1: Calculate Safety Stock**
The formula for calculating safety stock in a continuous review system is:
\[ z\sigma_{dLT}, \text{ where } \sigma_{dLT} = \sigma_d \sqrt{L}. \]
- **Given:**
- Standard deviation of weekly demand (\(\sigma_d\)) = 120 units
- Lead time (\(L\)) = 1 week
Using the standard normal table, for a 96% service level, the z-value is 1.75.
Therefore, the safety stock calculation is:
\[ 1.75 \times 120 \times \sqrt{1} = 210 \text{ units}. \]
**Step 2: Calculate Demand During Lead Time**
First, calculate weekly demand (\(\bar{d}\)):
\[ \bar{d} = \frac{\text{Demand}}{\text{Work Weeks per Year}} = \frac{52,000}{48} = 1,083 \text{ units}. \]
Now, calculate demand during lead time (\(\bar{dL}\)):
\[ \bar{dL} = 1,083 \times 1 = 1,083 \text{ units}. \]
**Step 3: Calculate Reorder Point**
The reorder point (\(\text{R}\)) is the sum of demand during lead time and safety stock:
\[ \text{R} = 1,083 + 210 = 1,293 \text{ units}. \]
This detailed process helps in determining the appropriate safety stock and reorder point to maintain a desired service level in inventory management.
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