Algebra

Linear Programming

Medium

applied

About linear programming problem (LPP), which of the following statements are correct?

(A) In a LPP, the linear inequalities or restrictions on the variables are called linear constraints.

(B) If the feasible region for an LPP is unbounded, then the maximum or minimum value of the objective function $Z = ax + by$ never exists.

(C) The feasible region for an LPP is always convex.

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

Choose the correct answer from the options given below:

(A), (B) and (D) only

(A), (C) and (D) only

(A), (B), (C) and (D)

(B) and (C) only

✅ Correct Option: 2

Statement (A) claims that linear inequalities or restrictions on the variables are called linear constraints.

This is the standard definition in linear programming. The inequalities that restrict the variables are termed linear constraints.

Statement (A) is correct.

Statement (B) claims that if the feasible region is unbounded, then the maximum or minimum value of the objective function $Z = ax + by$ never exists.

An unbounded feasible region extends infinitely in at least one direction.

Consider an unbounded region extending upward. While a maximum may not exist (as values increase indefinitely), a minimum can still exist at a boundary point.

The word "never" makes this statement false, as optimal values can exist for unbounded regions depending on the objective function and direction of unboundedness.

Statement (B) is incorrect.

Statement (C) claims that the feasible region for an LPP is always convex.

A feasible region is formed by the intersection of half-planes defined by linear constraints.

The intersection of convex sets (half-planes) always produces a convex set. Any line segment connecting two points in the feasible region lies entirely within the region.

Statement (C) is correct.

Statement (D) claims that the common region determined by all linear constraints is called the feasible region.

The feasible region is defined as the set of all points that simultaneously satisfy all the linear constraints of the problem.

This is the standard definition of a feasible region in linear programming.

Statement (D) is correct.

The correct statements are (A), (C), and (D).

2025: 27 May Shift 1

For the LPP: minimize $z = 6x + 3y$ subject to the constraints

$4x + y \geq 80$

$x + 5y \geq 115$

$3x + 2y \leq 150$

$x \geq 0, y \geq 0$ then the minimum value of z is

2026: 22 May Shift 2

The feasible region represented by the constraints $2x+y \le 12, x+2y \le 12, 4x+5y \ge 20, x,y \ge 0$ of LPP is

2025: 30 May Shift 2

The corner points of the bounded feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let z = px + qy where p, q > 0. Then the condition on p and q so that the maximum value of z occurs at (15, 15) and (0, 20) is

2026: 31 May Shift 2

The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ is :

2026: 29 May Shift 1

The corner points of the bounded feasible region for an LPP are (0, 0), (6, 0), (4, 3) and (0, 8). The objective function $Z=px+qy$ , $p,q>0$ has maximum value 360 at points (6, 0) and (4, 3). The value of $Z$ at (0, 8) is :

2023: 15 June Shift 2

Match List - I with List - II.

List - I	List - II
(A) The common region determined by all the constraints of LPP is called	(I) objective function
(B) Minimize $z = c_1x_1 + c_2x_2 + ..... + c_nx_n$ is	(II) convex set
(C) A solution that also satisfies the non-negative restrictions of a LPP is called	(III) feasible region
(D) The set of all feasible solutions of a LPP is a	(IV) feasible solution

Choose the correct answer from the options given below :

Solution

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