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The maximum level of inventory of an item is 100 and it is 100 and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continues throughout the year. Ordering cost is Rs. 100 per order and inventory carrying cost is Rs. 10 per item per month. Annual cost (in Rs.) of the plan, neglecting material cost, is:
- a)800
- b)2800
- c)4800
- d)6800
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The maximum level of inventory of an item is 100 and it is 100 and it ...
∴Number of cycles required per Year = 12 month/1.5 months = 8 cycles
Ordering cost = 8 * 100 = Rs. 800
Average inventory per cycle = 100/2 = 50
Inventory carrying cost = 50 * 12 * 10 = Rs. 6000
∴ Total cost = 800 + 6000 = 6800
Most Upvoted Answer
The maximum level of inventory of an item is 100 and it is 100 and it ...
Given data:
- Maximum inventory level = 100 items
- Replenishment rate = infinite
- Inventory becomes zero over 1.5 months due to consumption at a uniform rate
- Ordering cost = Rs. 100 per order
- Inventory carrying cost = Rs. 10 per item per month
To find:
- Annual cost of the plan, neglecting material cost
Assumptions:
- There are no stockouts or backorders
- Consumption rate and replenishment rate are constant throughout the year
Analysis:
1. We know that the inventory becomes zero over 1.5 months due to consumption at a uniform rate. This means that the consumption rate is equal to the replenishment rate.
2. Let's assume that the consumption rate and the replenishment rate are both x items per month.
3. The time taken to consume 100 items at the consumption rate (x items per month) is given by:
Time = (100 items) / (x items per month)
4. The time taken to replenish the inventory to 100 items at the replenishment rate (x items per month) is also given by:
Time = (100 items) / (x items per month)
5. Since the consumption rate and replenishment rate are equal, the time taken to consume and replenish the inventory to 100 items is the same.
6. Therefore, the total cycle time is:
Cycle Time = 1.5 months + 1.5 months = 3 months
7. The number of cycles in a year is given by:
Number of Cycles = (12 months) / (Cycle Time)
8. The annual ordering cost is given by:
Annual Ordering Cost = Number of Cycles * Ordering Cost per Order
9. The annual carrying cost is given by:
Annual Carrying Cost = (Maximum Inventory Level / 2) * Inventory Carrying Cost per Item per Month
10. The total annual cost is the sum of the annual ordering cost and the annual carrying cost.
Solution:
1. Calculate the time taken to consume and replenish the inventory to 100 items:
Time = (100 items) / (x items per month)
Time = 1.5 months
2. Calculate the cycle time:
Cycle Time = 1.5 months + 1.5 months = 3 months
3. Calculate the number of cycles in a year:
Number of Cycles = (12 months) / (Cycle Time) = 4
4. Calculate the annual ordering cost:
Annual Ordering Cost = Number of Cycles * Ordering Cost per Order
= 4 cycles * Rs. 100 per order
= Rs. 400
5. Calculate the annual carrying cost:
Annual Carrying Cost = (Maximum Inventory Level / 2) * Inventory Carrying Cost per Item per Month
= (100 items / 2) * Rs. 10 per item per month
= Rs. 500
6. Calculate the total annual cost:
Total Annual Cost = Annual Ordering Cost + Annual Carrying Cost
= Rs. 400 + Rs. 500
= Rs. 900
Conclusion:
The annual cost of the plan, neglecting material cost, is Rs. 900.
- Maximum inventory level = 100 items
- Replenishment rate = infinite
- Inventory becomes zero over 1.5 months due to consumption at a uniform rate
- Ordering cost = Rs. 100 per order
- Inventory carrying cost = Rs. 10 per item per month
To find:
- Annual cost of the plan, neglecting material cost
Assumptions:
- There are no stockouts or backorders
- Consumption rate and replenishment rate are constant throughout the year
Analysis:
1. We know that the inventory becomes zero over 1.5 months due to consumption at a uniform rate. This means that the consumption rate is equal to the replenishment rate.
2. Let's assume that the consumption rate and the replenishment rate are both x items per month.
3. The time taken to consume 100 items at the consumption rate (x items per month) is given by:
Time = (100 items) / (x items per month)
4. The time taken to replenish the inventory to 100 items at the replenishment rate (x items per month) is also given by:
Time = (100 items) / (x items per month)
5. Since the consumption rate and replenishment rate are equal, the time taken to consume and replenish the inventory to 100 items is the same.
6. Therefore, the total cycle time is:
Cycle Time = 1.5 months + 1.5 months = 3 months
7. The number of cycles in a year is given by:
Number of Cycles = (12 months) / (Cycle Time)
8. The annual ordering cost is given by:
Annual Ordering Cost = Number of Cycles * Ordering Cost per Order
9. The annual carrying cost is given by:
Annual Carrying Cost = (Maximum Inventory Level / 2) * Inventory Carrying Cost per Item per Month
10. The total annual cost is the sum of the annual ordering cost and the annual carrying cost.
Solution:
1. Calculate the time taken to consume and replenish the inventory to 100 items:
Time = (100 items) / (x items per month)
Time = 1.5 months
2. Calculate the cycle time:
Cycle Time = 1.5 months + 1.5 months = 3 months
3. Calculate the number of cycles in a year:
Number of Cycles = (12 months) / (Cycle Time) = 4
4. Calculate the annual ordering cost:
Annual Ordering Cost = Number of Cycles * Ordering Cost per Order
= 4 cycles * Rs. 100 per order
= Rs. 400
5. Calculate the annual carrying cost:
Annual Carrying Cost = (Maximum Inventory Level / 2) * Inventory Carrying Cost per Item per Month
= (100 items / 2) * Rs. 10 per item per month
= Rs. 500
6. Calculate the total annual cost:
Total Annual Cost = Annual Ordering Cost + Annual Carrying Cost
= Rs. 400 + Rs. 500
= Rs. 900
Conclusion:
The annual cost of the plan, neglecting material cost, is Rs. 900.
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The maximum level of inventory of an item is 100 and it is 100 and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continues throughout the year. Ordering cost is Rs. 100 per order and inventory carrying cost is Rs. 10 per item per month. Annual cost (in Rs.) of the plan, neglecting material cost, is:a)800 b)2800 c)4800 d)6800Correct answer is option 'D'. Can you explain this answer?
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The maximum level of inventory of an item is 100 and it is 100 and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continues throughout the year. Ordering cost is Rs. 100 per order and inventory carrying cost is Rs. 10 per item per month. Annual cost (in Rs.) of the plan, neglecting material cost, is:a)800 b)2800 c)4800 d)6800Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The maximum level of inventory of an item is 100 and it is 100 and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continues throughout the year. Ordering cost is Rs. 100 per order and inventory carrying cost is Rs. 10 per item per month. Annual cost (in Rs.) of the plan, neglecting material cost, is:a)800 b)2800 c)4800 d)6800Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum level of inventory of an item is 100 and it is 100 and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continues throughout the year. Ordering cost is Rs. 100 per order and inventory carrying cost is Rs. 10 per item per month. Annual cost (in Rs.) of the plan, neglecting material cost, is:a)800 b)2800 c)4800 d)6800Correct answer is option 'D'. Can you explain this answer?.
The maximum level of inventory of an item is 100 and it is 100 and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continues throughout the year. Ordering cost is Rs. 100 per order and inventory carrying cost is Rs. 10 per item per month. Annual cost (in Rs.) of the plan, neglecting material cost, is:a)800 b)2800 c)4800 d)6800Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The maximum level of inventory of an item is 100 and it is 100 and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continues throughout the year. Ordering cost is Rs. 100 per order and inventory carrying cost is Rs. 10 per item per month. Annual cost (in Rs.) of the plan, neglecting material cost, is:a)800 b)2800 c)4800 d)6800Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum level of inventory of an item is 100 and it is 100 and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continues throughout the year. Ordering cost is Rs. 100 per order and inventory carrying cost is Rs. 10 per item per month. Annual cost (in Rs.) of the plan, neglecting material cost, is:a)800 b)2800 c)4800 d)6800Correct answer is option 'D'. Can you explain this answer?.
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