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****Fundamental concepts, Simultaneous linear inequations - Basic Level**

**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.
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**Q1.**The solution set of the inequation 2x + y > 5, is

Solution

The solution set of the inequation 2x + y > 5, is Open half plane not containing the origin

The solution set of the inequation 2x + y > 5, is Open half plane not containing the origin

**Q2.**Inequation y - x ≤ 0 represents

Solution

Inequation y - x ≤ 0 represents the half plane that contains the positive x-axis

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

Solution

The half plane represented by the inequation is The half plane containing the point (h, k) and the points on ax + by = 4

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

Solution

If the constraints in a linear programming problem are changed then ,the problem is to be re-evaluated

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

Solution

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

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

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

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

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

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

Solution

The intermediate solutions of constraints must be checked by substituting them back into Constraint equations

The intermediate solutions of constraints must be checked by substituting them back into Constraint equations

**Q9.**Objective function of a L.P.P. is

Solution

Objective function of a L.P.P. is a function to be optimized

Objective function of a L.P.P. is a function to be optimized

**Q10.**A basic solution is called non-degenerate, if

Solution

A basic solution is called non-degenerate, if None of the basic variables is zero

A basic solution is called non-degenerate, if None of the basic variables is zero