Linear Programming - Online Test
Q1. 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
Answer : Option C
Explaination / Solution:
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.
Q2. 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
Answer : Option B
Explaination / Solution:
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 .
Q3. 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
Answer : Option C
Explaination / Solution:
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.
Q4. 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
Answer : Option D
Explaination / Solution:
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.
Q5. 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.
Answer : Option D
Explaination / Solution:
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 .
Q6. In a LPP, the objective function is always
Answer : Option B
Explaination / Solution:
In a LPP, the objective function is always linear. this is because these problems are always subjected to linear inequalities, where we maximise or minimise the linear functions.
Q7. The optimal value of the objective function Z = ax + by may or may not exist, if the feasible region for a LPP is
Answer : Option A
Explaination / Solution:
The optimal value of the objective function Z = ax + by may or may not exist, if the feasible region for a LPP is unbounded. This is because the maximum or minimum value of the objective function may not exist.Even if it exists it must occur in a corner pointof the feasible region.
Q8. In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same
Answer : Option C
Explaination / Solution:
In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same maximum value . If the problem has multiple optimal soliutions at the corner points, then both the points will have the same (maximum or minimum)value.
Q9. In linear programming problems the function whose maxima or minima are to be found is called
Answer : Option A
Explaination / Solution:
In linear programming problems the function whose maxima or minima are to be found is called Objective function . A linear function which has to be maximised or minimised is called as the linear objective function.
Q10. In linear programming problems the optimum solution
Answer : Option D
Explaination / Solution:
In linear programming problems the optimum solution satisfies a set of linear inequalities (called linear constraints) .
