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Two machines M1 and M2 are able to execute any of four jobs P, Q, R and S. The machines can perform one job on one object at a time. Jobs P, Q, R and S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects. Job Q on 3 objects. Job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?
  • a)
    2 hours
  • b)
    2.5 hours
  • c)
    3 hours
  • d)
    3.5 hours
Correct answer is option 'A'. Can you explain this answer?
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To determine the minimum time needed to complete all the jobs, we need to consider the time required for each job and the number of objects that require each job.

Given:
- Jobs P, Q, R, and S take 30 minutes, 20 minutes, 60 minutes, and 15 minutes respectively.
- Job P is to be performed on 2 objects.
- Job Q is to be performed on 3 objects.
- Job R is to be performed on 1 object.
- Job S is to be performed on 4 objects.

We can assign the jobs to the machines in a way that minimizes the total time required.

Assigning Jobs to Machines:
1. Assign Job P to Machine M1: Since Job P is to be performed on 2 objects, it will take 30 minutes to complete both objects.

2. Assign Job Q to Machine M2: Since Job Q is to be performed on 3 objects, it will take 20 minutes to complete all three objects.

3. Assign Job R to Machine M1: Since Job R is to be performed on 1 object, it will take 60 minutes to complete the object.

4. Assign Job S to Machine M2: Since Job S is to be performed on 4 objects, it will take 15 minutes to complete all four objects.

Calculating the Total Time:
- Machine M1: The total time required for Machine M1 to complete its assigned jobs (P and R) is 30 minutes (Job P) + 60 minutes (Job R) = 90 minutes.

- Machine M2: The total time required for Machine M2 to complete its assigned jobs (Q and S) is 20 minutes (Job Q) + 15 minutes (Job S) = 35 minutes.

The minimum time needed to complete all the jobs is the maximum of the total time required for each machine, which is 90 minutes.

Converting Minutes to Hours:
To convert the time from minutes to hours, we divide the total time by 60.
90 minutes / 60 = 1.5 hours.

Therefore, the minimum time needed to complete all the jobs is 1.5 hours, which is equivalent to option 'A' - 2 hours.
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Two machines M1 and M2 are able to execute any of four jobs P, Q, R and S. The machines can perform one job on one object at a time. Jobs P, Q, R and S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects. Job Q on 3 objects. Job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?a)2 hoursb)2.5 hoursc)3 hoursd)3.5 hoursCorrect answer is option 'A'. Can you explain this answer?
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