Linear Programming Test

Linear Programming

This is Linear Programming Test-01 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
A linear programming problem is one that is concerned with
  • A
    finding the lower limit of a linear function of several variables
  • B
    finding the optimal value (maximum or minimum) of a linear function of several variables
    Correct
  • C
    finding the limiting values of a linear function of several variables
  • D
    finding the upper limits of a linear function of several variables
2
Which of the following types of problems cannot be solved by linear programming methods
  • A
    Manufacturing problems
  • B
    Traffic signal control
    Correct
  • C
    Diet problems
  • D
    Transportation problems
3
In linear programming feasible region (or solution region) for the problem is
  • A
    The common region determined by all the x \( \geqslant \) 0, y \( \geqslant \) 0 and the objective function
  • B
    The common region determined by all the constraints including the non – negative constraints x \( \geqslant \) 0, y\( \geqslant \) 0
    Correct
  • C
    The common region determined by all the x \( \geqslant \) 0 and the objective function
  • D
    The common region determined by all the objective functions including the non – negative constraints x \( \geqslant \) 0, y \( \geqslant \) 0
4
In linear programming infeasible solutions
  • A
    fall on the x = 0 plane
  • B
    fall inside the a regular polygon
  • C
    fall inside the feasible region
  • D
    fall outside the feasible region
    Correct
5
In linear programming, optimal solution
  • A
    satisfies all the constraints as well as the objective function
    Correct
  • B
    satisfies all the constraints only
  • C
    is not unique
  • D
    maximizes the objective function only
6
Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities,
  • A
    optimal value must occur at the midpoints of the corner points (vertices) of the feasible region.
  • B
    None of these
  • C
    optimal value must occur at the centroid of the feasible region.
  • D
    optimal value must occur at a corner point (vertex) of the feasible region.
    Correct
7
Let R be the feasible region for a linear programming problem, and let Z = ax + by be the objective function. If R is bounded, then
  • A
    the objective function Z has no minimum value on R
  • B
    the objective function Z has only a minimum value on R
  • C
    the objective function Z has both a maximum and a minimum value on R
    Correct
  • D
    the objective function Z has only a maximum value on R
8
Let R be the feasible region for a linear programming problem,and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and
  • A
    each of these occurs at the centre of R.
  • B
    each of these occurs at some points except corner points of R.
  • C
    each of these occurs at a corner point (vertex) of R.
    Correct
  • D
    each of these occurs at themidpoints of the edges of R
9
A maximum or a minimum may not exist for a linear programming problem if
  • A
    if the objective function is continuous
  • B
    The feasible region is unbounded
    Correct
  • C
    if the constraints are non linear
  • D
    The feasible region is bounded
10
In Corner point method for solving a linear programming problem the first step is to
  • A
    Find the feasible region of the linear programming problem and determine its center points (vertices).
  • B
    Find the infeasible region of the linear programming problem and determine its complement
  • C
    Find the infeasible regions of the linear programming problem and determine theunion of the infeasible regions
  • D
    Find the feasible region of the linear programming problem and determine its corner points (vertices).
    Correct
11
In Corner point method for solving a linear programming problem the second step after finding the feasible region of the linear programming problem and determining its corner points is
  • A
    Evaluate the objective function Z = ax + by at the center point
  • B
    None of these
  • C
    Evaluate the objective function Z = ax + by at each corner point.
    Correct
  • D
    Evaluate the objective function Z = ax + by at the mid points
12
In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. If M and m respectively be the largest and smallest values at corner points then
  • A
    If the feasible region is unbounded, M and m respectively are the maximumand minimum values of the objective function
  • B
    None of these
  • C
    If the feasible region is bounded, M and m respectively are the minimum and maximum values of the objective function
  • D
    If the feasible region is bounded, M and m respectively are the maximum and minimum values of the objective function
    Correct
13
In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case feasible region is unbounded, M is the maximum value of the objective function if
  • A
    The open half plane determined by ax + by > M has no point in common with the feasible region
    Correct
  • B
    The open half plane determined by ax + by < M has no point in common with the feasible region
  • C
    The open half plane determined by ax + by > M has points in common with the feasible region
  • D
    None of these
14
In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case feasible region is unbounded, m is the minimum value of the objective function
  • A
    if the open half plane determined by ax + by < m has no point in common with the feasible region
    Correct
  • B
    if the open half plane determined by ax + by > m has no point in common with the feasible region
  • C
    if the open half plane determined by ax + by < m has points in common with the feasible region
  • D
    None of these
15
If two corner points of the feasible region are both optimal solutions of the same type, i.e., both produce the same maximum or minimum.
  • A
    then no point on the line segment joining these two points is an optimal solution of the opposite type
  • B
    then any point on the line segment joining these two points is also an optimal solution of the opposite type
  • C
    then any point on the line segment joining these two points is also an optimal solution of the same type
    Correct
  • D
    then no point on the line segment joining these two points is an optimal solution of thesame type