GATE2017 CE-1: GA-9

Question

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?

• A. $2$ hours
• B. $2.5$ hours
• C. $3$ hours
• D. $3.5$ hours

Comments

The machines can perform one job on one object at a time

can someone explain this  

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JAINchiNMay

one machine can perform only one job (P or Q or R or S) on a single object at a time.

means we cannot run some other job on some other object or even on the same object on the same machine at the same time .We have to wait for the job on that object to be completed and then that machine can perform some other job on some other object or on the same object.

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@Pranavpurkar

“one job on one object at a time”  suppose we have 10 objects and each requiring Job R of 60 minute then as in the question mention one job on one object at a time .so we cannot perform job R on two different object simultaneously even though we have two different machine, so in this case answer will be 10 hours not 5 hours am i correct?

Answer 1

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: $A$

Answer 2

P,Q,R, and S take 30 minutes, 20 minutes, 60 minutes and 15minutes each respectively.

 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

$\text{total time  for 1 machine} = 2 * 60 + 3*20+1*60 + 4 * 15=240 ~minutes=4 hrs$

$\therefore \text{total time for 2 machines} =2 hrs$