Linear Programming

Linear Programming is widely used in industries because it helps in

1. Solving trigonometric identities
2. Finding roots of polynomial equations
3. Efficient allocation of limited resources
4. Calculating matrix inverses

The graphical method of solving a Linear Programming Problem is suitable when the number of decision variables is

1. One only
2. Two
3. Three
4. More than three

The non-negativity constraints in a Linear Programming Problem are generally written as

1. x ≤ 0, y ≤ 0
2. x ≥ 0, y ≥ 0
3. x = 0, y = 0
4. x + y = 0

Which of the following is not a component of a Linear Programming Problem?

1. Objective function
2. Constraints
3. Decision variables
4. Quadratic equation

In a Linear Programming Problem, if the objective function has the same optimum value at two adjacent corner points of the feasible region, then

1. There is no optimal solution.
2. There is a unique optimal solution.
3. There are infinitely many optimal solutions on the line segment joining those corner points.
4. The feasible region becomes unbounded.

In the graphical method, after identifying the feasible region, the next step is to

1. Ignore the corner points.
2. Evaluate the objective function at each corner point.
3. Differentiate the objective function.
4. Solve the constraints algebraically only.

The objective function Z = 5x + 4y represents

1. A constraint
2. A linear objective function
3. A quadratic function
4. A nonlinear equation

If there is no common region satisfying all the given constraints, then the Linear Programming Problem is called

1. Bounded
2. Feasible
3. Infeasible
4. Optimal

A feasible region is said to be bounded if

1. It extends infinitely in all directions.
2. It lies inside a closed region.
3. It contains only one point.
4. It contains no corner points.

Which of the following inequalities represents the half-plane below the line x + y = 6?

1. x + y ≥ 6
2. x + y ≤ 6
3. x - y ≤ 6
4. x - y ≥ 6

In the graphical method of solving a Linear Programming Problem, the optimal value of the objective function occurs at

1. Any interior point
2. Any boundary point
3. A corner (vertex) of the feasible region
4. The origin only

The common region satisfying all the constraints of a Linear Programming Problem is called the

1. Objective function
2. Feasible region
3. Optimal solution
4. Solution set of equations

Which of the following is a linear constraint?

1. x^2 + y ≤ 5
2. xy ≤ 6
3. 2x + 3y ≤ 12
4. √x + y ≤ 7

The function to be maximized or minimized in a Linear Programming Problem is called the

1. Constraint
2. Objective function
3. Feasible region
4. Corner point

Linear Programming is a mathematical technique used to

1. Solve quadratic equations
2. Optimize (maximize or minimize) a linear objective function subject to linear constraints
3. Find derivatives of functions
4. Calculate determinants