Fundamental concepts, Simultaneous linear inequations - Basic Level

Dear Readers,

Linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming. .

Q1. The solution set of the inequation 2x + y > 5, is
•  Half plane that contains the origin
•  Open half plane not containing the origin
•  Whole xy–plane except the points lying on the line 2x + y = 5
•  None of these
Solution
The solution set of the inequation 2x + y > 5, is Open half plane not containing the origin

Q2.Inequation y - x ≤ 0 represents
•  The half plane that contains the positive x-axis
•  Closed half plane above the line y = x which contains positive y-axis
•  Half plane that contains the negative x-axis
•  None of these
Solution
Inequation y - x ≤ 0 represents the half plane that contains the positive x-axis

Q3.  If a point (h, k) satisfies an inequation ax + by ≥ 4, then the half plane represented by the inequation is
•  The half plane containing the point (h, k) but excluding the points on ax + by = 4
•  The half plane containing the point (h, k) and the points on ax + by = 4
•  Whole xy-plane
•  None of these
Solution
The half plane represented by the inequation is The half plane containing the point (h, k) and the points on ax + by = 4

Q4. If the constraints in a linear programming problem are changed
•  The problem is to be re-evaluated
•  Solution is not defined
•  The objective function has to be modified
•  The change in constraints is ignored.
Solution
If the constraints in a linear programming problem are changed then ,the problem is to be re-evaluated

Q5.The optimal value of the objective function is attained at the points
•  Given by intersection of inequations with the axes only
•  Given by intersection of inequation with x-axis only
•  Given by corner points of the feasible region
•  None of these
Solution
The optimal value of the objective function is attained at the points given by corner points of the feasible region

Q6. The position f points O (0, 0) and P (2, –2) in the region of graph of inequations 2x - 3y < 5, will be
•  O inside and P outside
•  O and P both inside
• O and P both outside
•  O outside and P inside
Solution
The position f points O (0, 0) and P (2, –2) in the region of graph of inequations 2x - 3y < 5, will be O inside and P outside

Q7.If the number of available constraints is 3 and the number of parameters to be optimized is 4, then
•  The objective function can be optimized
•  The constraints are short in number
•  The solution is problem oriented
•  None of these
Solution
If the number of available constraints is 3 and the number of parameters to be optimized is 4, then the constraints are short in number

Q8.The intermediate solutions of constraints must be checked by substituting them back into
•  Object function
•  Constraint equations
•  Not required
•  None of these
Solution
The intermediate solutions of constraints must be checked by substituting them back into Constraint equations

Q9.Objective function of a L.P.P. is
•  A constraint
•  A function to be optimized
•  A relation between the variables
•  None of these
Solution
Objective function of a L.P.P. is a function to be optimized

Q10. A basic solution is called non-degenerate, if
•  All these basic variables are zero
•  None of the basic variables is zero
•  At least one of the basic variable is zero
•  None of these
Solution
A basic solution is called non-degenerate, if None of the basic variables is zero

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