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A firm produces and used 2400 items annually. The cost of setting up for production is R 850 and the weekly production rate is 100 units. The production cost is Rs. 5 per item. The annual storage and carrying is 10% of average inventory. The time, each optimum production run would take, will be Ops: A. 12 months B. 9 months C. 6 months D. 1 month?
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A firm produces and used 2400 items annually. The cost of setting up f...
Optimum Production Run Time Calculation
Given data:
- Annual production: 2400 items
- Setup cost: R 850
- Weekly production rate: 100 units
- Production cost per item: Rs. 5
- Annual storage and carrying: 10% of average inventory
Calculate the optimum production run time based on the given data.
Step 1: Determine the Economic Order Quantity (EOQ)
EOQ is the optimum order quantity that minimizes the total cost of ordering and holding inventory. It is calculated using the following formula:
EOQ = sqrt((2*D*S)/H)
Where,
D = Annual demand (2400 items)
S = Setup cost (R 850)
H = Holding cost per unit per year (10% of Rs. 5 = Rs. 0.50)
EOQ = sqrt((2*2400*850)/0.50) = 1225.19
Step 2: Calculate the number of production runs per year
The number of production runs per year can be calculated as follows:
Number of production runs = (Annual demand) / (EOQ)
Number of production runs = 2400 / 1225.19 = 1.96
Since we cannot have a fractional number of runs, we will round it up to 2.
Step 3: Calculate the production time per run
The production time per run can be calculated as follows:
Production time per run = (EOQ) / (Weekly production rate)
Production time per run = 1225.19 / 100 = 12.25 weeks
Step 4: Convert the production time to months
Since the question asks for the optimum production run time in months, we will convert the production time to months:
Production time per run in months = (Production time per run) / (Number of weeks in a month)
Production time per run in months = 12.25 / 4 = 3.06 months
Step 5: Calculate the optimum production run time
The optimum production run time is the time taken for one production run. It can be calculated as follows:
Optimum production run time = (Number of production runs per year) * (Production time per run in months)
Optimum production run time = 2 * 3.06 = 6.12 months
Therefore, the optimum production run time is 6 months (Option C).
Given data:
- Annual production: 2400 items
- Setup cost: R 850
- Weekly production rate: 100 units
- Production cost per item: Rs. 5
- Annual storage and carrying: 10% of average inventory
Calculate the optimum production run time based on the given data.
Step 1: Determine the Economic Order Quantity (EOQ)
EOQ is the optimum order quantity that minimizes the total cost of ordering and holding inventory. It is calculated using the following formula:
EOQ = sqrt((2*D*S)/H)
Where,
D = Annual demand (2400 items)
S = Setup cost (R 850)
H = Holding cost per unit per year (10% of Rs. 5 = Rs. 0.50)
EOQ = sqrt((2*2400*850)/0.50) = 1225.19
Step 2: Calculate the number of production runs per year
The number of production runs per year can be calculated as follows:
Number of production runs = (Annual demand) / (EOQ)
Number of production runs = 2400 / 1225.19 = 1.96
Since we cannot have a fractional number of runs, we will round it up to 2.
Step 3: Calculate the production time per run
The production time per run can be calculated as follows:
Production time per run = (EOQ) / (Weekly production rate)
Production time per run = 1225.19 / 100 = 12.25 weeks
Step 4: Convert the production time to months
Since the question asks for the optimum production run time in months, we will convert the production time to months:
Production time per run in months = (Production time per run) / (Number of weeks in a month)
Production time per run in months = 12.25 / 4 = 3.06 months
Step 5: Calculate the optimum production run time
The optimum production run time is the time taken for one production run. It can be calculated as follows:
Optimum production run time = (Number of production runs per year) * (Production time per run in months)
Optimum production run time = 2 * 3.06 = 6.12 months
Therefore, the optimum production run time is 6 months (Option C).
Community Answer
A firm produces and used 2400 items annually. The cost of setting up f...
Solution:
Given data:
Annual demand (D) = 2400 items
Set up cost (S) = R850
Weekly production rate (P) = 100 units
Production cost (C) = Rs. 5 per item
Carrying cost (H) = 10% of average inventory
Let us calculate the optimum production run time using the economic order quantity (EOQ) model.
1. Calculating the EOQ
EOQ formula is given by:
EOQ = √((2DS)/H)
where,
D = Annual demand
S = Set up cost
H = Carrying cost
EOQ = Economic order quantity
Substituting the given values, we get:
EOQ = √((2*2400*850)/0.1)
EOQ = 1960.6
Hence, the optimum production quantity is 1960 units.
2. Calculating the number of production runs
Number of production runs = Annual demand / EOQ
Number of production runs = 2400 / 1960.6
Number of production runs = 1.224
Therefore, we need to produce 1960 units 1.224 times in a year.
3. Calculating the optimum production run time
Optimum production run time = EOQ / P
Optimum production run time = 1960 / 100
Optimum production run time = 19.6 weeks
Since we need to produce 1960 units 1.224 times in a year, the total time required for production is:
Total production time = 19.6 * 1.224
Total production time = 23.96 weeks
Therefore, the optimum production run time is approximately 6 months (i.e., 23.96 weeks).
Hence, the answer is option C.
Given data:
Annual demand (D) = 2400 items
Set up cost (S) = R850
Weekly production rate (P) = 100 units
Production cost (C) = Rs. 5 per item
Carrying cost (H) = 10% of average inventory
Let us calculate the optimum production run time using the economic order quantity (EOQ) model.
1. Calculating the EOQ
EOQ formula is given by:
EOQ = √((2DS)/H)
where,
D = Annual demand
S = Set up cost
H = Carrying cost
EOQ = Economic order quantity
Substituting the given values, we get:
EOQ = √((2*2400*850)/0.1)
EOQ = 1960.6
Hence, the optimum production quantity is 1960 units.
2. Calculating the number of production runs
Number of production runs = Annual demand / EOQ
Number of production runs = 2400 / 1960.6
Number of production runs = 1.224
Therefore, we need to produce 1960 units 1.224 times in a year.
3. Calculating the optimum production run time
Optimum production run time = EOQ / P
Optimum production run time = 1960 / 100
Optimum production run time = 19.6 weeks
Since we need to produce 1960 units 1.224 times in a year, the total time required for production is:
Total production time = 19.6 * 1.224
Total production time = 23.96 weeks
Therefore, the optimum production run time is approximately 6 months (i.e., 23.96 weeks).
Hence, the answer is option C.
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A firm produces and used 2400 items annually. The cost of setting up for production is R 850 and the weekly production rate is 100 units. The production cost is Rs. 5 per item. The annual storage and carrying is 10% of average inventory. The time, each optimum production run would take, will be Ops: A. 12 months B. 9 months C. 6 months D. 1 month?
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A firm produces and used 2400 items annually. The cost of setting up for production is R 850 and the weekly production rate is 100 units. The production cost is Rs. 5 per item. The annual storage and carrying is 10% of average inventory. The time, each optimum production run would take, will be Ops: A. 12 months B. 9 months C. 6 months D. 1 month? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A firm produces and used 2400 items annually. The cost of setting up for production is R 850 and the weekly production rate is 100 units. The production cost is Rs. 5 per item. The annual storage and carrying is 10% of average inventory. The time, each optimum production run would take, will be Ops: A. 12 months B. 9 months C. 6 months D. 1 month? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A firm produces and used 2400 items annually. The cost of setting up for production is R 850 and the weekly production rate is 100 units. The production cost is Rs. 5 per item. The annual storage and carrying is 10% of average inventory. The time, each optimum production run would take, will be Ops: A. 12 months B. 9 months C. 6 months D. 1 month?.
A firm produces and used 2400 items annually. The cost of setting up for production is R 850 and the weekly production rate is 100 units. The production cost is Rs. 5 per item. The annual storage and carrying is 10% of average inventory. The time, each optimum production run would take, will be Ops: A. 12 months B. 9 months C. 6 months D. 1 month? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A firm produces and used 2400 items annually. The cost of setting up for production is R 850 and the weekly production rate is 100 units. The production cost is Rs. 5 per item. The annual storage and carrying is 10% of average inventory. The time, each optimum production run would take, will be Ops: A. 12 months B. 9 months C. 6 months D. 1 month? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A firm produces and used 2400 items annually. The cost of setting up for production is R 850 and the weekly production rate is 100 units. The production cost is Rs. 5 per item. The annual storage and carrying is 10% of average inventory. The time, each optimum production run would take, will be Ops: A. 12 months B. 9 months C. 6 months D. 1 month?.
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