A linear programming problem is one that is concerned with
A
finding the limiting values of a linear function of several variables
B
finding the optimal value (maximum or minimum) of a linear function of several variables
C
finding the lower limit of a linear function of several variables
D
finding the upper limits of a linear function of several variables
A linear programming problem is one that is concerned with finding the optimal value (maximum or minimum) of a linear function of several variables .
Which of the following types of problems cannot be solved by linear programming methods
A
Transportation problems
B
Traffic signal control
C
Diet problems
D
Manufacturing problems
Traffic signal control types of problems cannot be solved by linear programming methods, because there is no need for optimization in such problems.
In linear programming feasible region (or solution region) for the problem is
A
The common region determined by all the x 0 and the objective function
B
The common region determined by all the constraints including the non – negative constraints x 0, y 0
C
The common region determined by all the objective functions including the non – negative constraints x 0, y 0
D
The common region determined by all the x 0, y 0 and the objective function
In linear programming feasible region (or solution region) for the problem is given by the common region determined by all the constraints including the non – negative constraints x 0, y 0
In linear programming infeasible solutions
A
fall outside the feasible region
B
fall inside the feasible region
C
fall inside the a regular polygon
D
fall on the x = 0 plane
In linear programming infeasible solutions fall outside the feasible region. In other words, it the region other than the feasible region is called the infeasible region.
In linear programming, optimal solution
A
is not unique
B
maximizes the objective function only
C
satisfies all the constraints only
D
satisfies all the constraints as well as the objective function
In linear programming, any point in the feasible region which gives that gives the optimal value (maximum or minimum) of the objective function is called optimal solution. In other words, it satisfies all the constraints as well as the objective function.
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
optimal value must occur at the centroid of the feasible region.
C
None of these
D
optimal value must occur at a corner point (vertex) of the feasible region.
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 then , optimal value must occur at a corner point (vertex) of the feasible region.
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
D
the objective function Z has only a maximum value on R
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 each of these occur at the corner point (vertex) of R.
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 some points except corner points of R.
B
each of these occurs at a corner point (vertex) of R.
C
each of these occurs at the centre of R.
D
each of these occurs at the midpoints of the edges of R
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 each of these occurs at a corner point (vertex) of R.
A maximum or a minimum may not exist for a linear programming problem if
A
The feasible region is unbounded
B
The feasible region is bounded
C
If the constraints are non-linear
D
If the objective function is continuous
A maximum or a minimum may or may not exist for a linear programming problem if the feasible region is unbounded. However if it exits it must occur at the corner points of R.
In Corner point method for solving a linear programming problem the first step is to
A
Find the infeasible regions of the linear programming problem and determine theunion of the infeasible regions
B
Find the feasible region of the linear programming problem and determine its corner points (vertices).
C
Find the feasible region of the linear programming problem and determine its center points (vertices).
D
Find the infeasible region of the linear programming problem and determine its complement
In Corner point method for solving a linear programming problem the first step is : To find the feasible region of the linear programming problem and determine its corner points (vertices) either by inspection or by solving the two equations of the lines intersecting at that point.
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 each corner point.
B
None of these
C
Evaluate the objective function Z = ax + by at the mid points
D
Evaluate the objective function Z = ax + by at the center point
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 : To evaluate the objective function Z = ax + by at each corner point.
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 bounded, M and m respectively are the minimum and maximum values of the objective function
B
None of these
C
If the feasible region is unbounded, M and m respectively are the maximum and minimum 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
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 Mand m respectively be the largest and smallest values at corner points then If the feasible region is bounded, M and m respectively are the maximum and minimum values of the objective function .
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
B
The open half plane determined by ax + by < M has no point in common with the feasible region
C
None of these
D
The open half plane determined by ax + by > M has points in common with the feasible region
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 the open half plane determined by ax + by > M has no point in common with the feasible region . Otherwise, Z has no maximum value.
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 points in common with the feasible region
B
if the open half plane determined by ax + by < m has no point in common with the feasible region
C
None of these
D
if the open half plane determined by ax + by > m has no point in common with the feasible region
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 if the open half plane determined by ax + by < m has no point in common with the feasible region . Otherwise, Z has no minimum point.
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 same type
C
then no point on the line segment joining these two points is an optimal solution of the same type
D
then any point on the line segment joining these two points is also an optimal solution of the opposite type
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 , then any point on the line segment joining these two points is also an optimal solution of the same type .