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An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).
Correct answer is '520'. Can you explain this answer?
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An assignment problem is solved to minimize the total processing time ...
Assignment Problem
The assignment problem is a mathematical problem in which a set of jobs needs to be assigned to a set of machines, with the objective of minimizing the total processing time. In this case, we have four jobs (1, 2, 3, and 4) and four machines.
Original Minimum Total Processing Time
The original minimum total processing time is given as 500 minutes. This means that the assignment of jobs to machines has been optimized in such a way that the total processing time is minimized.
Change in Design
Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. This means that the new processing time for Job 4 on each machine is the original processing time plus 20 minutes.
Revised Minimum Total Processing Time
To calculate the revised minimum total processing time, we need to consider the new processing time for Job 4 on each machine.
Calculating Revised Processing Time
1. Calculate the original processing time for Job 4 on each machine.
2. Add 20 minutes to the original processing time for Job 4 on each machine to get the revised processing time.
3. Calculate the new total processing time by summing up the processing times of all jobs on their respective machines.
Let's assume the original processing time for Job 4 on each machine is x minutes.
Revised processing time = x + 20 minutes
New total processing time = (Total processing time of Job 1 + Total processing time of Job 2 + Total processing time of Job 3 + Revised processing time of Job 4)
Since Job 1, Job 2, and Job 3 remain unchanged, their total processing times will remain the same. Therefore, we only need to consider the revised processing time of Job 4.
New total processing time = (Total processing time of Job 1 + Total processing time of Job 2 + Total processing time of Job 3 + Revised processing time of Job 4)
= (Total processing time of Job 1 + Total processing time of Job 2 + Total processing time of Job 3 + (x + 20))
Since the original minimum total processing time was 500 minutes, we can write the equation as:
500 = (Total processing time of Job 1 + Total processing time of Job 2 + Total processing time of Job 3 + (x + 20))
Solving for x
To find the value of x, we need to consider the processing times of Job 1, Job 2, and Job 3. However, since we do not have any information about these processing times, we cannot determine the exact value of x.
But we can still determine the revised minimum total processing time by assuming the worst-case scenario, where the processing times of Job 1, Job 2, and Job 3 are all zero.
In this case, the equation becomes:
500 = (0 + 0 + 0 + (x + 20))
500 = x + 20
x = 480
Calculating Revised Minimum Total Processing Time
Now that we have the value of x, we can calculate the revised minimum total processing time by substituting the value of x into the equation:
New total processing time = (Total processing time of Job 1 + Total
The assignment problem is a mathematical problem in which a set of jobs needs to be assigned to a set of machines, with the objective of minimizing the total processing time. In this case, we have four jobs (1, 2, 3, and 4) and four machines.
Original Minimum Total Processing Time
The original minimum total processing time is given as 500 minutes. This means that the assignment of jobs to machines has been optimized in such a way that the total processing time is minimized.
Change in Design
Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. This means that the new processing time for Job 4 on each machine is the original processing time plus 20 minutes.
Revised Minimum Total Processing Time
To calculate the revised minimum total processing time, we need to consider the new processing time for Job 4 on each machine.
Calculating Revised Processing Time
1. Calculate the original processing time for Job 4 on each machine.
2. Add 20 minutes to the original processing time for Job 4 on each machine to get the revised processing time.
3. Calculate the new total processing time by summing up the processing times of all jobs on their respective machines.
Let's assume the original processing time for Job 4 on each machine is x minutes.
Revised processing time = x + 20 minutes
New total processing time = (Total processing time of Job 1 + Total processing time of Job 2 + Total processing time of Job 3 + Revised processing time of Job 4)
Since Job 1, Job 2, and Job 3 remain unchanged, their total processing times will remain the same. Therefore, we only need to consider the revised processing time of Job 4.
New total processing time = (Total processing time of Job 1 + Total processing time of Job 2 + Total processing time of Job 3 + Revised processing time of Job 4)
= (Total processing time of Job 1 + Total processing time of Job 2 + Total processing time of Job 3 + (x + 20))
Since the original minimum total processing time was 500 minutes, we can write the equation as:
500 = (Total processing time of Job 1 + Total processing time of Job 2 + Total processing time of Job 3 + (x + 20))
Solving for x
To find the value of x, we need to consider the processing times of Job 1, Job 2, and Job 3. However, since we do not have any information about these processing times, we cannot determine the exact value of x.
But we can still determine the revised minimum total processing time by assuming the worst-case scenario, where the processing times of Job 1, Job 2, and Job 3 are all zero.
In this case, the equation becomes:
500 = (0 + 0 + 0 + (x + 20))
500 = x + 20
x = 480
Calculating Revised Minimum Total Processing Time
Now that we have the value of x, we can calculate the revised minimum total processing time by substituting the value of x into the equation:
New total processing time = (Total processing time of Job 1 + Total
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Community Answer
An assignment problem is solved to minimize the total processing time ...
Given data
No. of Machine (M) = M1 , M2 , M3 , M4
No. of job (J) = J1 , J2 , J3 , J4
Total minimum processing time = 500 min
Processing time increased for each job = 20 min
Hence the revised total minimum processing time = 520 min
Hence, the correct answer is 520.
No. of Machine (M) = M1 , M2 , M3 , M4
No. of job (J) = J1 , J2 , J3 , J4
Total minimum processing time = 500 min
Processing time increased for each job = 20 min
Hence the revised total minimum processing time = 520 min
Hence, the correct answer is 520.
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An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).Correct answer is '520'. Can you explain this answer?
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An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).Correct answer is '520'. 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 An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).Correct answer is '520'. 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 An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).Correct answer is '520'. Can you explain this answer?.
An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).Correct answer is '520'. 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 An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).Correct answer is '520'. 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 An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).Correct answer is '520'. Can you explain this answer?.
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