Production and Industrial Engineering
GATE PI topic:operation-research PYQs
Build your understanding with focused practice from past exam papers.
How to practice topic:operation-research
Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.
Questions 1–10 of 21. Imported answers require independent review unless marked reviewed.
Question 14
Open questionPIMCQ1 markNeeds review
Which ONE of the following options represents correctly ALL the constraints resulting in the feasible region for the given linear programming problem as shown in the figure?
Note: Figure not to scale
Your answerChoose one option.
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Open questionPIMCQ1 markNeeds review
In the given weighted graph, the weights represent distance between the corresponding vertices. The shortest distance between vertex A and vertex E is d. The number of paths with distance d is p.
The value of d/p is ______.
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Open questionPIMCQ2 marksNeeds review
In an M/M/1 queuing system, the customers arrive at a rate of 3 per minute, and the average number of customers in the system is
at steady state. Assume that the server utilization is less than 1.Which ONE of the following is the average time a customer spends in the system (in minutes) at steady state?
Your answerChoose one option.
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Open questionPINAT2 marksNeeds review
A company must allocate oil produced from their two plants to meet all the demands of two markets. The cost per litre of allocation from plant
to market
is denoted by
. The market demand
, plant production capacity
and
values are given in the table. | Market 1 ( ) | Market 2 ( ) | Capacity in litres |
|---|---|---|---|
Plant 1 ( ) | | | |
Plant 2 ( ) | | | |
Demand in litres | | | |
The company hired an intern to formulate an optimization model to decide on the quantity (
) to be allocated from plant
to market
and the formulation is given below:Minimize
Subject to
The optimal value of the objective function of the linear programming problem formulated by the intern is _____ (in integer).
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Open questionPIMCQ1 markNeeds review
The starting simplex table of a linear programming problem is given below, where
,
,
and
are the slack variables. The objective of the problem isMaximize
The leaving variable among the basic variables is
Basic | | | | | | | Solution |
|---|---|---|---|---|---|---|---|
| 6 | 3 | 1 | 0 | 0 | 0 | 36 |
| 2 | 1 | 0 | 1 | 0 | 0 | 40 |
| | 3 | 0 | 0 | 1 | 0 | 2 |
| 0 | 3 | 0 | 0 | 0 | 1 | 3 |
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Open questionPINAT2 marksNeeds review
Three plants P₁, P₂ and P₃ produce 6, 1 and 9 thousand liters of fruit juice, respectively. The produced fruit juice is transported to three distribution centers D₁, D₂ and D₃ with requirement of 7, 5 and 4 thousand liters of juice, respectively. The transportation cost (in hundreds of Rupees) from each plant to each distribution center is given in the table. The total transportation cost (in hundreds of Rupees) in initial basic feasible solution using Vogel’s approximation method is ________. (Answer in integer)
| D₁ | D₂ | D₃ | Supply |
|---|---|---|---|---|
P₁ | 2 | 3 | 11 | 6 |
P₂ | 1 | 0 | 6 | 1 |
P₃ | 5 | 8 | 15 | 9 |
Demand | 7 | 5 | 4 | |
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Open questionPIMCQ1 markNeeds review
Which of the following is NOT an assumption of a linear programming problem?
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Open questionPIMCQ1 markNeeds review
In a single server Markovian queuing system, if the customers arrive following the Poisson distribution, then the inter-arrival time follows
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Open questionPIMCQ2 marksNeeds review
Consider the following linear programming problem with two decision variables
and
. There are three constraints involving resources R1, R2 and R3 as indicated.Maximize
Subject to
R1
R2
R3
The optimal solution of the problem is:
and
.For which one of the following options, the shadow price of the resource(s) will have non-zero value?
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Open questionPIMCQ2 marksNeeds review
The dual of a LPP is
subject to,
and
for
The objective function of the primal is
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