Mechanical Engineering
GATE ME topic:operations-research PYQs
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How to practice topic:operations-research
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Questions 1–10 of 30. Imported answers require independent review unless marked reviewed.
Question 46
Open questionMEMCQ2 marksNeeds review
An objective function
of primal variables (
and
) is described below:Minimize
subject to
is the objective function of the dual of
.
, and
represent the corresponding dual variables.Which one of the following options represents the correct form of
?Your 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 65
Open questionMENAT2 marksNeeds review
The activities of a PERT network and their corresponding activity time estimates (in weeks) i.e., optimistic (
), most likely (
), and pessimistic (
) are given in the table below.Activity | | | |
|---|---|---|---|
1–2 | 2 | 4 | 12 |
1–3 | 2 | 4 | 6 |
1–4 | 3 | 4 | 11 |
2–5 | 3 | 6 | 9 |
3–4 | 2 | 5 | 14 |
3–5 | 3 | 3 | 3 |
4–5 | 3 | 6 | 15 |
5–6 | 2 | 5 | 8 |
The expected project length is ________ weeks (in integer).
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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 65
Open questionMENAT2 marksNeeds review
A project involves eight activities with the presence relationship and duration as shown in the table below. The slack for the activity D is _____ hours (answer in integer).
Activity | Immediate predecessor | Duration (hours) |
|---|---|---|
A | - | 4 |
B | A | 8 |
C | A | 5 |
D | B | 2 |
E | B | 7 |
F | C | 6 |
G | D | 3 |
H | E, F, G | 9 |
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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 35
Open questionMEMCQ1 markNeeds review
A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queue system follows the Poisson distribution with a mean of 5 jobs/hour. The service time of the server is exponentially distributed with a mean of 6 minutes. In steady state operation of the queue system, the probability that the server is not busy at any point in time is
Your 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 39
Open questionMEMCQ2 marksNeeds review
At the current basic feasible solution (bfs)
(
), the simplex method yields the following form of a linear programming problem in standard form.
Here the objective function is written as a function of the non-basic variables. If the simplex method moves to the adjacent bfs
(
) that best improves the objective function, which of the following represents the objective function at
, assuming that the objective function is written in the same manner as above?Your 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 65
Open questionMENAT2 marksNeeds review
In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each retailer are tabulated below. The supply chain manager wishes to minimize the total cost of transportation across the supply chain.
| Retailer I | Retailer II | Retailer III | Retailer IV | Capacity |
|---|---|---|---|---|---|
Supplier A | 11 | 16 | 19 | 13 | 300 |
Supplier B | 5 | 10 | 7 | 8 | 300 |
Supplier C | 12 | 14 | 17 | 11 | 300 |
Supplier D | 8 | 15 | 11 | 9 | 300 |
Demand | 300 | 300 | 300 | 300 | |
The optimal cost of satisfying the total demand from all retailers is _____ rupees (answer in integer).
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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 14
Open questionMEMCQ1 markNeeds review
Which one of the options given represents the feasible region of the linear programming model:
Your answerChoose one option.
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Open questionMEMCQ1 markNeeds review
In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is
Your 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 41
Open questionMEMCQ2 marksNeeds review
Parts P1-P7 are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time required for carrying out both the operations for all 7 parts is ______ hours.
Part | Milling (hours) | Polishing (hours) |
|---|---|---|
P1 | 8 | 6 |
P2 | 3 | 2 |
P3 | 3 | 4 |
P4 | 4 | 6 |
P5 | 5 | 7 |
P6 | 6 | 4 |
P7 | 2 | 1 |
Your 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 42
Open questionMEMCQ2 marksNeeds review
Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity G is ____________ hours.
Activity | Time (hours) | Immediate predecessors |
|---|---|---|
A | 2 | — |
B | 3 | — |
C | 2 | — |
D | 4 | A |
E | 5 | B |
F | 4 | B |
G | 3 | C |
H | 10 | D, E |
I | 5 | F |
J | 8 | G |
K | 3 | H, I, J |
Your answerChoose one option.
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