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QUESTION: 1

If the system of constraints has no point which satisfies all the constraints and non-negativity restrictions then the solution of a LPP is an

Solution:

QUESTION: 2

The optimum value of the objective function is attained at the points

Solution:

The optimal value of the objective function is attained at the points given by corner points of the feasible region.

QUESTION: 3

The maximum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≤ 160, 5x + 2y ≤ 200, x + 2y ≤ 80 ;

x, y ≥ 0 attains at

Solution:

QUESTION: 4

A feasible solution of a LPP if it also optimizes the objective function is called

Solution:

QUESTION: 5

Shape of the feasible region formed by the following constraints is x + y ≤ 10, x + y ≥ 6, x ≥ 0, y ≥ 0

Solution:

x + y ≤ 10

x + y = 10

For x = 0, y = 10

x + y ≥ 6, x + y = 6

For x = 0, y =6

Hence, the image will be the trapezium.

QUESTION: 6

Region represented by x ≥ 0, y ≥ 0 is

Solution:

QUESTION: 7

Find the maximum value of z = 3x + 4y subject to constraints x + y ≤ 4 , x ≥ 0 and y ≥ 0

Solution:

QUESTION: 8

Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

Solution:

QUESTION: 9

The set of all feasible solutions of a LPP is a ____ set.

Solution:

The set of feasible solutions to an LP (feasible region) forms a (possibly unbounded) convex set.

QUESTION: 10

Which of the following sets are convex ?

Solution:

{(x,y) : y≥2 , y≤4} is the region between two parallel lines, so any line segment joining any two points in it lies in it. Hence, it is the convex set.

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