Mechanical Engineering
GATE ME topic:operations-research PYQs
Build your understanding with focused practice from past exam papers.
Questions 21–30 of 30. Imported answers require independent review unless marked reviewed.
Question 54
Open questionMENAT2 marksNeeds review
Five jobs (J1, J2, J3, J4 and J5) need to be processed in a factory. Each job can be assigned to any of the five different machines (M1, M2, M3, M4 and M5). The time durations taken (in minutes) by the machines for each of the jobs, are given in the table. However, each job is assigned to a specific machine in such a way that the total processing time is minimum. The total processing time is ______ minutes.
| M1 | M2 | M3 | M4 | M5 |
|---|---|---|---|---|---|
J1 | 40 | 30 | 50 | 50 | 58 |
J2 | 26 | 38 | 60 | 26 | 38 |
J3 | 40 | 34 | 28 | 24 | 30 |
J4 | 28 | 40 | 40 | 32 | 48 |
J5 | 28 | 32 | 38 | 22 | 44 |
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 55
Open questionMENAT2 marksNeeds review
A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below:
Activity | Immediate predecessor | Estimated duration (weeks) |
|---|---|---|
P | - | 5 |
Q | - | 1 |
R | Q | 2 |
S | P, R | 4 |
T | P | 6 |
U | S, T | 3 |
If all activities other than S take the estimated amount of time, the maximum duration (in weeks) of the activity S without delaying the completion of the project is __________
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Open questionMEMCQ2 marksNeeds review
The problem of maximizing
subject to constraints
,
,
and
hasYour answerChoose one option.
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Open questionMENAT2 marksNeeds review
The minimum value of 3x + 5y such that:
3x + 5y ≤ 15
4x + 9y ≤ 8
13x + 2y ≤ 2
x ≥ 0, y ≥ 0
is ______.
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Open questionMENAT2 marksNeeds review
The arc lengths of a directed graph of a project are shown in the figure. The shortest path length from node 1 to node 6 is ______.
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Open questionME-2MCQ1 markNeeds review
For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?
Your answerChoose one option.
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Open questionME-2MCQ2 marksNeeds review
A product made in two factories, P and Q, is transported to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix:
Factory | R | S |
|---|---|---|
P | 10 | 7 |
Q | 3 | 4 |
Factory P produces 7 units and factory Q produces 9 units of the product. Each destination requires 8 units. If the north-west corner method provides the total transportation cost as
(in Rupees) and the optimized (the minimum) total transportation cost is
(in Rupees), then
, in Rupees, isYour answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 49
Open questionME-2NAT2 marksNeeds review
A project starts with activity A and ends with activity F. The precedence relation and durations of the activities are as per the following table:
Activity | Immediate predecessor | Duration (days) |
|---|---|---|
A | – | 4 |
B | A | 3 |
C | A | 7 |
D | B | 14 |
E | C | 4 |
F | D, E | 9 |
The minimum project completion time (in days) is ____________
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Open questionME-1NAT2 marksNeeds review
Two models, P and Q, of a product earn profits of Rs. 100 and Rs. 80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, to maximize profit, the number of units of P to be produced is ________
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 51
Open questionME-2NAT2 marksNeeds review
Maximize
,
subject to
,
,
.
In the starting Simplex table,
and
are non-basic variables and the value of
is zero. The value of
in the next Simplex table is ____________Log in to check the answer
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