Which of the following are correct about the linear programming problem(LPP)?

(A) The objective function is always linear.

(B) A corner point of a feasible region is a point in the region which is the intersection of two boundary lines.

(C) The common region determined by all the linear constraints of a LPP is called the feasible region.

(D) If an LPP admits optimal solution at two points then its optimal values occurs at an infinite number of points.

Choose the correct answer from the options given below:

(A) The objective function is always linear.

In Linear Programming, the objective function must be linear. A linear function has the form $Z = ax + by$ where variables appear only to the first power.

For example: Maximize $Z = 3x + 4y$

This statement is correct.

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(B) A corner point of a feasible region is a point in the region which is the intersection of two boundary lines.

Corner points (vertices) occur where two boundary lines intersect. These points are critical because optimal solutions in linear programming occur at corner points of the feasible region.

For example, if Line 1: $x + y = 10$ and Line 2: $x - y = 2$ intersect at $(6, 4)$, this intersection point is a corner point.

This statement is correct.

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(C) The common region determined by all the linear constraints of a LPP is called the feasible region.

The feasible region is the area where all constraints are satisfied simultaneously. It represents all possible solutions that meet every constraint in the problem.

For constraints such as:

$x + y \leq 10$

$x \geq 0$

$y \geq 0$

The feasible region is where all three inequalities hold true.

This statement is correct.

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(D) If an LPP admits optimal solution at two points then its optimal values occurs at an infinite number of points.

When the optimal value occurs at two different corner points, every point on the line segment connecting these corners also yields the same optimal value. Since a line segment contains infinitely many points, there are infinitely many optimal solutions.

For example, if the optimal value $Z = 20$ occurs at points $A(2,4)$ and $B(4,2)$, then all points on the line segment between $A$ and $B$ also give $Z = 20$.

This statement is correct.

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All four statements (A), (B), (C), and (D) are correct.

Therefore, the correct answer is: (A), (B), (C) and (D)