GATE MA Linear Programming PYQs & Answers

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Questions 1–10 of 39. Imported answers require independent review unless marked reviewed.

Topic practice 39 questionsPage 1 of 4

Consider the following assignment problem where

are tasks,

are agents and the cost matrix is given by

Which of the following statements is/are TRUE for an optimal assignment?

Your answerSelect all correct options. You can choose more than one.

The cost is 9.

Agent P is assigned to task Y.

Agent Q is assigned to task X.

Agent R is assigned to task Y.

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Consider the following Linear Programming Problem (LP):

The maximum value of

in the above LP is equal to ________. (answer in integer)

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For a transportation problem, let

denote the unit cost of the cell

. Assume that

and

. Let

and

, represent the simplex multipliers associated with any basis corresponding to the unit cost

. Assume that

and

. The relative cost coefficient

is the difference between the current solution and the new improved solution. If

and

, then which one of the following is TRUE?

Your answerChoose one option.

and

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Let

. If

is an optimal solution of the Linear Programming Problem:

then the maximum value of

is equal to ________. (answer in integer)

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For the linear programming problem:

Maximize

Subject to

consider the following two statements:

S1: If

and

, then

forms an optimal basis.

S2: If

and

, then

forms an optimal basis.

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

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Consider the balanced transportation problem with three sources

, and four destinations

, for minimizing the total transportation cost whose cost matrix is as follows:

					Supply
	2	6	20	11
	12	7	4	10
	8	14	16	11	5
Demand		10

where

. If the associated cost to the starting basic feasible solution obtained by using the North-West corner rule is 290, then which of the following is/are correct?

Your answerSelect all correct options. You can choose more than one.

The optimal cost of the transportation problem is 260

The optimal cost of the transportation problem is 290

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Consider the following regions:

Then, which of the following is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

The maximum value of

is 3 on the region

The maximum value of

is 5 on the region

The maximum value of

is 3 on the region

The maximum value of

is 4 on the region

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Consider the linear programming problem (LPP):

Maximize

Subject to

Given that

forms the optimal basis of the LPP with basis matrix

and respective

. If

is the optimal solution of the dual of the LPP, then which of the following is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

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Consider the following Linear Programming Problem

The optimal value of the problem

is equal to

Your answerChoose one option.

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The maximum value of

subject to the constraints

is equal to

(round off to TWO decimal places)

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GATE MA Linear Programming PYQs

How to practice Linear Programming

Question 26

Question 33

Question 46

Question 63

Question 14

Question 24

Question 25

Question 49

Question 25

Question 58