GATE ME topic:operations-research PYQs & Answers — Page 2 — Exam Papers

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Questions 11–20 of 30. Imported answers require independent review unless marked reviewed.

Topic practice 30 questionsPage 2 of 3

A manufacturing unit produces two products P1 and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit earned. The maximum quantity available per day for M1, M2 and M3 is also provided. The maximum possible profit per day is ₹__________.

	M1	M2	M3	Profit per piece (₹)
P1	2	2	0	150
P2	3	1	2	100
Maximum quantity available per day	70	50	40

Your answerChoose one option.

A.

5000

B.

4000

C.

3000

D.

6000

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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).

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A project consists of five activities (A, B, C, D and E). The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediate predecessor(s) are listed in the table. The expected time of the project completion is __________ weeks (in integer).

Activity	Optimistic time	Most likely time	Pessimistic time	Immediate predecessor(s)
A	4	5	6	None
B	1	3	5	A
C	1	2	3	A
D	2	4	6	C
E	3	4	5	B, D

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A PERT network has 9 activities on its critical path. The standard deviation of each activity on the critical path is 3. The standard deviation of the critical path is

Your answerChoose one option.

A.

3

B.

9

C.

27

D.

81

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Activities A, B, C and D for the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) distribution, and are independent of each other.

Activity	A	B	C	D
Mean (days)	6	11	8	15
Variance (days )	4	9	4	9

The probability that the project will be completed within 40 days is ______ (round off to two decimal places).

(Note: Probability is a number between 0 and 1).

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Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of 12 jobs/hour. The process time of the workstation is exponentially distributed with a mean of 4 minutes. The expected number of jobs at the workstation at any given point of time is ______ (round off to the nearest integer).

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In the Critical Path Method (CPM), the cost-time slope of an activity is given by

Your answerChoose one option.

A.

B.

C.

D.

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Consider the following network of activities, with each activity named A–L, illustrated in the nodes of the network. The number of hours required for each activity is shown alongside the nodes. The slack on the activity L, is ________hours.

Diagram for Mechanical Engineering question 23

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Two business owners Sheta and Ashok run their business in two different states. Each of them, independent of the other, produces two products A and B, sells them at Rs. 2,000 per kg and Rs. 3,000 per kg, respectively, and uses Linear Programming to determine the optimal quantity of A and B to maximize their respective daily revenue. Their constraints are as follows: i) for each business owner, the production process is such that the daily production of A has to be at least as much B, and the upper limit for production of B is 10 kg per day, and ii) the respective state regulations restrict Sheta’s production of A to less than 20 kg per day, and Ashok’s production of A to less than 15 kg per day. The demand of both A and B in both the states is very high and everything produced is sold.

The absolute value of the difference in daily (optimal) revenue of Sheta and Ashok is ______ thousand Rupees (round off to 2 decimal places).

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The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship “X < Y, Z” means that X is predecessor of activities Y and Z. The time to complete the activities along the critical path is ______ weeks.

Activity	Duration (Weeks)	Precedence Relationship
A	5	A < B, C, D
B	7	B < E, F, G
C	10	C < I
D	6	D < G
E	3	E < H
F	9	F < I
G	7	G < I
H	4	H < I
I	2	---

Your answerChoose one option.

A.

17

B.

21

C.

23

D.

25

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