GATE PI concept:linear-programming PYQs & Answers

Questions 1–8 of 8. Imported answers require independent review unless marked reviewed.

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

Diagram for Production and Industrial Engineering question 14

Your answerChoose one option.

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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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The starting simplex table of a linear programming problem is given below, where

and

are the slack variables. The objective of the problem is

Maximize

The leaving variable among the basic variables is

						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

Your answerChoose one option.

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Which of the following is NOT an assumption of a linear programming problem?

Your answerChoose one option.

Proportionality

Additivity

Integrality

Certainty

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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

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?

Your answerChoose one option.

R1, R2 and R3

R1 and R2

R2 and R3

R1 only

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Consider the linear programming problem:

Maximize

subject to

(C₁)

(C₂)

(C₃)

The optimal solution is given as

and

. The dual variables of constraints C₁, C₂ and C₃ are

and

, respectively. The optimal values of dual variables are

and

. The value of parameter P in the objective function is____________. [round off to one decimal place]

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The Bellman’s principle of optimality is related to

Your answerChoose one option.

Linear programming problem

Transportation problem

Dynamic programming problem

Assignment problem

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A company manufactures products P and Q in quantities

and

, respectively, using two resources. The following Linear Programming Problem (LPP) is formulated to maximize the profit Z.

Maximize

subject to

(for Resource 1)

(for Resource 2) and

The shadow price for Resource 2 is

Your answerChoose one option.

2/3

4/3

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GATE PI concept:linear-programming PYQs

How to practice concept:linear-programming

Question 14

Question 58

Question 27

Question 23

Question 42

Question 63

Question 21

Question 33