Algebra

Linear Programming

Medium

applied

For the linear programming problem (LPP),

$Maximize Z = 7x + 9y$ , subject to constraints,

$x - y \le -1, -x + y \le 0, x, y \ge 0.$

Which of the following is correct?

The feasible region is bounded.

The optimal value of the objective function exists at the point (1, 1).

The optimal value of the objective function is 16.

No feasible region exists.

✅ Correct Option: 4

In any Linear Programming Problem, the feasible region is the area where all constraints are satisfied simultaneously. If no such region exists, no optimal solution can be found.

The given constraints are:

$x - y \le -1$

$-x + y \le 0$

$x \ge 0$

$y \ge 0$

Rewriting these in clearer form:

$x - y \le -1$ can be rewritten as $y \ge x + 1$

$-x + y \le 0$ can be rewritten as $y \le x$

$x \ge 0$

$y \ge 0$

For any point to be in the feasible region, it must satisfy both:

$y \ge x + 1$ and $y \le x$

This requires: $x + 1 \le y \le x$

Which simplifies to: $x + 1 \le x$

This gives: $1 \le 0$

This is a contradiction.

Since no point $(x, y)$ can satisfy both constraints simultaneously, no feasible region exists.

Without a feasible region, there can be no bounded region, no feasible points, and no optimal value.

Therefore, the correct answer is: No feasible region exists.

2025: 3 June Shift 1

If the feasible region of an LPP is bounded and the corresponding objective function is $z = 5x - 9y$ , then the objective function attains:

2025: 14 May Shift 1

The corner points of the feasible region associated with the LPP: Maximise $Z = px + qy$ , $p,q > 0$ subject to $2x + y \leq 10$ , $x + 3y \leq 15$ , $x, y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then

2022: 4 Aug Shift 1

The corner points of feasible region are:

A. (0, 240)

B. (0, 0)

C. (300, 0)

D. (120, 180)

E. (180, 120)

Choose the correct answer from the options given below:

2026: 31 May Shift 2

If the corner points of the bounded feasible region for an LPP are $(5,0), (0,4), (0,2), (3,4)$ , and $(0,7)$ , then the minimum value of the objective function $z = 2x+5y$ occurs at :

2023: 30 May Shift 3

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

2026: 18 May Shift 2

The feasible region of an LPP is a bounded region by vertices (4, 18), (6, 12), (40, 0) and (15, 0). Then the point (15, 15) lies in the

A. open half plane of $x+2y<40$ .

B. closed half plane of $3x+y\ge 30$ .

C. closed half plane of $4x+3y\ge 60$ .

D. feasible region of the given LPP.

Choose the correct answer from the options given below:

For the linear programming problem (LPP), MaximizeZ=7x+9yMaximize Z = 7x + 9yMaximizeZ=7x+9y, subject to constraints, x−y≤−1,−x+y≤0,x,y≥0.x - y \le -1, -x + y \le 0, x, y \ge 0.x−y≤−1,−x+y≤0,x,y≥0. Which of the following is correct?

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

For the linear programming problem (LPP),

$Maximize Z = 7x + 9y$ , subject to constraints,

$x - y \le -1, -x + y \le 0, x, y \ge 0.$

Which of the following is correct?