GATE MA Linear Programming PYQs & Answers — Page 4

Questions 31–39 of 39. Imported answers require independent review unless marked reviewed.

Consider the following cost matrix of assigning four jobs to four persons:

Persons / Jobs	J₁	J₂	J₃	J₄
P₁	5	8	6	10
P₂	2	5	4	8
P₃	6	7	6	9
P₄	6	9	8	10

Then the minimum cost of the assignment problem subject to the constraint that job J₄ is assigned to person P₂, is ______.

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By the Simplex method, the optimal table of the linear programming problem:

where

are real constants, is

		3	0	0
Basic variable					Solution
	1	0	2	-1	6
	0	1	-1	1	2
	0	0	2	1	-

Then the value of

is ______.

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For a linear programming problem, which one of the following statements is FALSE?

Your answerChoose one option.

If a constraint is an equality, then the corresponding dual variable is unrestricted in sign

Both primal and its dual can be infeasible

If primal is unbounded, then its dual is infeasible

Even if both primal and dual are feasible, the optimal values of the primal and the dual can differ

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Consider the Linear Programming Problem (LP):

Maximize

Subject to

where

is a constant. If

is the only optimal solution, then

Your answerChoose one option.

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A certain commodity is produced by the manufacturing plants

and

whose capacities are 6 and 5 units, respectively. The commodity is shipped to markets

and

whose requirements are 1, 2, 3 and 5 units, respectively. The transportation cost per unit from plant

to market

is as follows:

					Supply
	1	3	5	8	6
	2	5	6	7	5
Demand	1	2	3	5

Then the optimal cost of transportation is _________.

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Consider the linear programming problem (LP): Maximize

Subject to

is unrestricted in sign. Then the LP has

Your answerChoose one option.

no optimal solution

only one basic feasible solution and that is optimal

more than one basic feasible solution and a unique optimal solution

infinitely many optimal solutions

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For a linear programming problem (LP) and its dual, which one of the following is NOT TRUE?

Your answerChoose one option.

The dual of the dual is primal

If the primal LPP has an unbounded objective function, then the dual LPP is infeasible

If the primal LPP is infeasible, then the dual LPP must have unbounded objective function

If the primal LPP has a finite optimal solution, then the dual LPP also has a finite optimal solution

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Consider the following transportation problem. The entries inside the cells denote per unit cost of transportation from the origins to the destinations.

Origin	Destination 1	Destination 2	Destination 3	Supply
1	4	3	6	20
2	7	10	5	30
3	8	9	7	50
Demand	10	30	60

The optimal cost of transportation equals ________.

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Consider the linear programming problem (LP):

is an optimal solution of the above LPP with

, then the largest value of

(rounded to 2 decimal places) for which

remains optimal equals ________.

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GATE MA Linear Programming PYQs

Question 48

Question 52

Question 12

Question 39

Question 55

Question 24

Question 25

Question 54

Question 55