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Two machine $M1$ 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?

1. $2$ hours
2. $2.5$ hours
3. $3$ hours
4. $3.5$ hours

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Migrated from GO Civil 8 months ago by Arjun

At first, machine $M_1$ will be associated with 2 object of job $P (30\times 2=60$ minutes$)$ and simultaneously, machine $M_2$ will do $1$ object of job $R$. So, in $1$ hour jobs $P$ and $R$ are completed.

Now, machine $M_1$ will do $3$ objects of job $Q$ for next hour $(20\times 3=60$ minutes$)$ while, machine $M_2$ will simultaneously complete $4$ objects of job $S(15\times 4= 60$ minutes$).$

Thus, minimum time needed to complete all the jobs $= 1 + 1 = 2$ hours.

Correct Answer: $A$
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