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In the production shop of a company the breakdown of the machine is found to follow poisson distribution with an average rate of 3 machines per hour. Break down time at one machine
costs 40 rupees per hour to the company. The company hires a repairman who demands rupees 20 per hour and will repair the broken down machines following the exponential distribution at the rate of 4 per hour. The total cost involved in hiring the repairman is
costs 40 rupees per hour to the company. The company hires a repairman who demands rupees 20 per hour and will repair the broken down machines following the exponential distribution at the rate of 4 per hour. The total cost involved in hiring the repairman is
- a)250
- b)180
- c)130
- d)210
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In the production shop of a company the breakdown of the machine is fo...
λ = 3/hr
μ = 4/hr
Total waiting time in system for one machine is
= 
= 1 hour
= 1 hourThe down time of 3 machines is
= 3 × 1 = 3 hour
Down time cost = 40 × 3 = Rs 120
Repairman cost = 3 × 20 = Rs 60
Total cost = 120 60 = Rs 180
= 3 × 1 = 3 hour
Down time cost = 40 × 3 = Rs 120
Repairman cost = 3 × 20 = Rs 60
Total cost = 120 60 = Rs 180
Most Upvoted Answer
In the production shop of a company the breakdown of the machine is fo...
Given:
- Breakdown of machine follows Poisson distribution with an average rate of 3 machines per hour.
- Cost of breakdown time at one machine is 40 rupees per hour to the company.
- A repairman is hired who demands 20 rupees per hour.
- Repairman repairs the broken down machines following the exponential distribution at the rate of 4 per hour.
To find:
- Total cost involved in hiring the repairman.
Solution:
1. Expected number of breakdowns in an hour:
- The breakdown of the machine follows Poisson distribution with an average rate of 3 machines per hour.
- Therefore, the expected number of breakdowns in an hour is λ=3.
2. Cost of breakdown in an hour:
- Cost of breakdown time at one machine is 40 rupees per hour to the company.
- Therefore, the cost of breakdown in an hour is 40*λ=40*3=120 rupees.
3. Expected number of repairs in an hour:
- Repairman repairs the broken down machines following the exponential distribution at the rate of 4 per hour.
- Therefore, the expected number of repairs in an hour is μ=4.
4. Cost of repairs in an hour:
- Repairman demands 20 rupees per hour.
- Therefore, the cost of repairs in an hour is 20*μ=20*4=80 rupees.
5. Total cost involved in hiring the repairman:
- Total cost involved in hiring the repairman is the sum of the cost of breakdown and the cost of repairs in an hour.
- Total cost = 120 + 80 = 200 rupees.
Therefore, the correct option is (B) 180 rupees.
- Breakdown of machine follows Poisson distribution with an average rate of 3 machines per hour.
- Cost of breakdown time at one machine is 40 rupees per hour to the company.
- A repairman is hired who demands 20 rupees per hour.
- Repairman repairs the broken down machines following the exponential distribution at the rate of 4 per hour.
To find:
- Total cost involved in hiring the repairman.
Solution:
1. Expected number of breakdowns in an hour:
- The breakdown of the machine follows Poisson distribution with an average rate of 3 machines per hour.
- Therefore, the expected number of breakdowns in an hour is λ=3.
2. Cost of breakdown in an hour:
- Cost of breakdown time at one machine is 40 rupees per hour to the company.
- Therefore, the cost of breakdown in an hour is 40*λ=40*3=120 rupees.
3. Expected number of repairs in an hour:
- Repairman repairs the broken down machines following the exponential distribution at the rate of 4 per hour.
- Therefore, the expected number of repairs in an hour is μ=4.
4. Cost of repairs in an hour:
- Repairman demands 20 rupees per hour.
- Therefore, the cost of repairs in an hour is 20*μ=20*4=80 rupees.
5. Total cost involved in hiring the repairman:
- Total cost involved in hiring the repairman is the sum of the cost of breakdown and the cost of repairs in an hour.
- Total cost = 120 + 80 = 200 rupees.
Therefore, the correct option is (B) 180 rupees.
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In the production shop of a company the breakdown of the machine is found to follow poisson distribution with an average rate of 3 machines per hour. Break down time at one machinecosts 40 rupees per hour to the company. The company hires a repairman who demands rupees 20 per hour and will repair the broken down machines following the exponential distribution at the rate of 4 per hour. The total cost involved in hiring the repairman isa)250b)180c)130d)210Correct answer is option 'B'. Can you explain this answer?
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In the production shop of a company the breakdown of the machine is found to follow poisson distribution with an average rate of 3 machines per hour. Break down time at one machinecosts 40 rupees per hour to the company. The company hires a repairman who demands rupees 20 per hour and will repair the broken down machines following the exponential distribution at the rate of 4 per hour. The total cost involved in hiring the repairman isa)250b)180c)130d)210Correct answer is option 'B'. 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 In the production shop of a company the breakdown of the machine is found to follow poisson distribution with an average rate of 3 machines per hour. Break down time at one machinecosts 40 rupees per hour to the company. The company hires a repairman who demands rupees 20 per hour and will repair the broken down machines following the exponential distribution at the rate of 4 per hour. The total cost involved in hiring the repairman isa)250b)180c)130d)210Correct answer is option 'B'. 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 In the production shop of a company the breakdown of the machine is found to follow poisson distribution with an average rate of 3 machines per hour. Break down time at one machinecosts 40 rupees per hour to the company. The company hires a repairman who demands rupees 20 per hour and will repair the broken down machines following the exponential distribution at the rate of 4 per hour. The total cost involved in hiring the repairman isa)250b)180c)130d)210Correct answer is option 'B'. Can you explain this answer?.
In the production shop of a company the breakdown of the machine is found to follow poisson distribution with an average rate of 3 machines per hour. Break down time at one machinecosts 40 rupees per hour to the company. The company hires a repairman who demands rupees 20 per hour and will repair the broken down machines following the exponential distribution at the rate of 4 per hour. The total cost involved in hiring the repairman isa)250b)180c)130d)210Correct answer is option 'B'. 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 In the production shop of a company the breakdown of the machine is found to follow poisson distribution with an average rate of 3 machines per hour. Break down time at one machinecosts 40 rupees per hour to the company. The company hires a repairman who demands rupees 20 per hour and will repair the broken down machines following the exponential distribution at the rate of 4 per hour. The total cost involved in hiring the repairman isa)250b)180c)130d)210Correct answer is option 'B'. 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 In the production shop of a company the breakdown of the machine is found to follow poisson distribution with an average rate of 3 machines per hour. Break down time at one machinecosts 40 rupees per hour to the company. The company hires a repairman who demands rupees 20 per hour and will repair the broken down machines following the exponential distribution at the rate of 4 per hour. The total cost involved in hiring the repairman isa)250b)180c)130d)210Correct answer is option 'B'. Can you explain this answer?.
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