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In machine shop, pins of 15 mm diameter are produced at a rate of 1000 per month and the same is consumed at a rate of 500 per month.The production and consumption continue simultaneously till the maximum inventory is reached. Then inventory is allowed to reduce to zero due to consumption. The lot size of production is 1000. If backlog is not allowed, the maximum inventory level is
[2007]
- a)400
- b)500
- c)600
- d)700
Correct answer is option 'B'. Can you explain this answer?
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In machine shop, pins of 15 mm diameter are produced at a rate of 1000...
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In machine shop, pins of 15 mm diameter are produced at a rate of 1000...
Given:
- Diameter of pins produced = 15 mm
- Production rate = 1000 pins per month
- Consumption rate = 500 pins per month
- Lot size of production = 1000 pins
To find:
- Maximum inventory level
Approach:
1. Calculate the net production rate (production rate - consumption rate).
2. Calculate the time taken to produce a lot size of pins (lot size / net production rate).
3. Calculate the maximum number of lot sizes that can be produced in a month (production rate / lot size).
4. Calculate the maximum inventory level (maximum number of lot sizes * lot size).
Calculation:
1. Net production rate = production rate - consumption rate
= 1000 - 500
= 500 pins per month
2. Time taken to produce a lot size of pins = lot size / net production rate
= 1000 / 500
= 2 months
3. Maximum number of lot sizes that can be produced in a month = production rate / lot size
= 1000 / 1000
= 1 lot
4. Maximum inventory level = maximum number of lot sizes * lot size
= 1 * 1000
= 1000 pins
However, it is mentioned that the inventory is allowed to reduce to zero due to consumption. Hence, the maximum inventory level is limited to the lot size of production, which is 1000 pins.
Therefore, the correct answer is option B) 500.
- Diameter of pins produced = 15 mm
- Production rate = 1000 pins per month
- Consumption rate = 500 pins per month
- Lot size of production = 1000 pins
To find:
- Maximum inventory level
Approach:
1. Calculate the net production rate (production rate - consumption rate).
2. Calculate the time taken to produce a lot size of pins (lot size / net production rate).
3. Calculate the maximum number of lot sizes that can be produced in a month (production rate / lot size).
4. Calculate the maximum inventory level (maximum number of lot sizes * lot size).
Calculation:
1. Net production rate = production rate - consumption rate
= 1000 - 500
= 500 pins per month
2. Time taken to produce a lot size of pins = lot size / net production rate
= 1000 / 500
= 2 months
3. Maximum number of lot sizes that can be produced in a month = production rate / lot size
= 1000 / 1000
= 1 lot
4. Maximum inventory level = maximum number of lot sizes * lot size
= 1 * 1000
= 1000 pins
However, it is mentioned that the inventory is allowed to reduce to zero due to consumption. Hence, the maximum inventory level is limited to the lot size of production, which is 1000 pins.
Therefore, the correct answer is option B) 500.
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In machine shop, pins of 15 mm diameter are produced at a rate of 1000 per month and the same is consumed at a rate of 500 per month.The production and consumption continue simultaneously till the maximum inventory is reached. Then inventory is allowed to reduce to zero due to consumption. The lot size of production is 1000. If backlog is not allowed, the maximum inventory level is[2007]a)400b)500c)600d)700Correct answer is option 'B'. Can you explain this answer?
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