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Capacities of production of an item over 3 consecutive months in regular time are 100,100 and 80 and in overtime are 20, 20 and 40. The demands over those 3 months are 90, 130 and 110. The cost of production in regular time and overtime are respectively Rs. 20 per item and Rs. 24 per item. Inventory carrying cost is Rs. 2 per item month. The levels of starting and final inventory are nil. Backorder is not permitted. For minimum cost of plan, the level of planned production in overtime in the third month is
[2007]
  • a)
    40
  • b)
    30
  • c)
    20
  • d)
    0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Capacities of production of an item over 3 consecutive months in regul...
For minimum total cost the entire regular time production capacity has to be used.
Hence, total over time capacity required = (90 + 130 + 110) – (100+ 100 + 80) = 50
20 Overtime units will be used up in first 2 weeks. Hence 30 overtime units are needed to fulfill the 3rd month demand.
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Most Upvoted Answer
Capacities of production of an item over 3 consecutive months in regul...
Given:
- Capacities of production in regular time: 100, 100, 80
- Capacities of production in overtime: 20, 20, 40
- Demands over 3 months: 90, 130, 110
- Cost of production in regular time: Rs. 20 per item
- Cost of production in overtime: Rs. 24 per item
- Inventory carrying cost: Rs. 2 per item per month
- Starting and final inventory levels: nil
- Backorder not permitted

Objective:
To determine the level of planned production in overtime in the third month for minimum cost of plan.

Step-by-step Solution:


1. Calculate the regular time production needed:

- Regular time production = Demand - Inventory
- Month 1: Regular time production = 90 - 0 = 90
- Month 2: Regular time production = 130 - 0 = 130
- Month 3: Regular time production = 110 - 0 = 110

2. Calculate the overtime production needed:

- Overtime production = Demand - Regular time production
- Month 1: Overtime production = 90 - 90 = 0
- Month 2: Overtime production = 130 - 130 = 0
- Month 3: Overtime production = 110 - 110 = 0

3. Calculate the cost of regular time production:

- Month 1: Cost of regular time production = Regular time production * Cost per item = 90 * 20 = Rs. 1800
- Month 2: Cost of regular time production = 130 * 20 = Rs. 2600
- Month 3: Cost of regular time production = 110 * 20 = Rs. 2200

4. Calculate the cost of overtime production:

- Month 1: Cost of overtime production = Overtime production * Cost per item = 0 * 24 = Rs. 0
- Month 2: Cost of overtime production = 0 * 24 = Rs. 0
- Month 3: Cost of overtime production = 0 * 24 = Rs. 0

5. Calculate the carrying cost of inventory:

- Carrying cost of inventory = Inventory * Carrying cost per item per month
- Month 1: Carrying cost of inventory = 0 * 2 = Rs. 0
- Month 2: Carrying cost of inventory = 0 * 2 = Rs. 0
- Month 3: Carrying cost of inventory = 0 * 2 = Rs. 0

6. Calculate the total cost:

- Total cost = Cost of regular time production + Cost of overtime production + Carrying cost of inventory
- Month 1: Total cost = 1800 + 0 + 0 = Rs. 1800
- Month 2: Total cost = 2600 + 0 + 0 = Rs. 2600
- Month 3: Total cost = 2200 + 0 + 0 = Rs. 2200

7. Determine the level
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Capacities of production of an item over 3 consecutive months in regular time are 100,100 and 80 and in overtime are 20, 20 and 40. The demands over those 3 months are 90, 130 and 110. The cost of production in regular time and overtime are respectively Rs. 20 per item and Rs. 24 per item. Inventory carrying cost is Rs. 2 per item month. The levels of starting and final inventory are nil. Backorder is not permitted. For minimum cost of plan, the level of planned production in overtime in the third month is[2007]a)40b)30c)20d)0Correct answer is option 'B'. Can you explain this answer?
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