Algebra

Linear Programming

Medium

common

Consider the Linear Programming Problem

Maximize $z = x + y$

Subject to the constraints $x - y \leq -1$ , $x \geq y$ , $x \geq 0, y \geq 0$

Then which one of the following is TRUE?

Maximum $z = 3$ at $(1, 2)$

There is no solution

Maximum $z = 15$ at $(7, 8)$

Maximum $z = 10$ at all points on the line $x - y = -1$

✅ Correct Option: 2

The problem requires finding points $(x, y)$ that satisfy all constraints simultaneously, then maximizing $z = x + y$ .

The constraints are:

$x - y \leq -1$
$x \geq y$
$x \geq 0$
$y \geq 0$

From the first constraint $x - y \leq -1$ :

$x - y \leq -1$

$x \leq y - 1$

This means $x < y$ (x must be less than y)

From the second constraint:

$x \geq y$

This means x must be greater than or equal to y.

Comparing these two conditions:

From constraint 1: $x < y$

From constraint 2: $x \geq y$

These two conditions are contradictory. A value cannot be both less than y and greater than or equal to y simultaneously.

Since the constraints contradict each other, no point $(x, y)$ can satisfy all constraints at the same time.

Therefore, there is no feasible region and no solution to this linear programming problem.

The answer is: There is no solution.

2025: 27 May Shift 1

The corner points of the bounded feasible region determined by the system of linear constraints are (15,0), (40,0), (4,18) and (6, 12). If objective function is Z = 30x + 20y, then the sum of the maximum and the minimum values of Z is

2025: 14 May Shift 2

Consider the linear programming problem(LPP):

Minimize $Z = x + y$

$x + 2y \leq 4,$

$3x + y \geq 3,$

$4x + 3y \geq 6,$

$x, y \geq 0.$

Which of the following is correct for the above linear programming problem (LPP):

(A) The LPP has a bounded feasible region.

(B) The LPP has a unique optimal solution.

(D) The corner points of the feasible region are (3/2, 0), (3/5, 6/5), (2/5, 6/5) and (4, 0)

Choose the correct answer from the options given below:

2025: 26 May Shift 2

For the objective function Z=-4x + 6y subject to the constraints 3x + 2y ≥ 5, 7x + 2y ≤ 9, x ≥ 0, y ≥ 0, the maximum value of Z occurs at $(a, b)$ and the minimum value of Z occurs at $(p, q)$ then the value of $\frac{a}{p} + \frac{b}{q}$ is:

2026: 29 May Shift 1

The maximum value of $z=5x+3y$ subjected to the constraints $2x+3y \ge 60, 2x+y \le 40; x,y \ge 0$ is:

2026: 21 May Shift 2

Which one of the following set of constraints depicted the shaded region given below?

2025: 22 May Shift 2

The maximum value of the objective function $z = 10x + 15y$ of an L.P.P. subjected to the constraints

$2x + 4y \leq 8$ ,

$3x + y \leq 6$ ,

$-x - y \geq -4$ ,

$x \geq 0$ , $y \geq 0$ is:

Consider the Linear Programming Problem Maximize z=x+yz = x + yz=x+y Subject to the constraints x−y≤−1x - y \leq -1x−y≤−1, x≥yx \geq yx≥y, x≥0,y≥0x \geq 0, y \geq 0x≥0,y≥0 Then which one of the following is TRUE?

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Consider the Linear Programming Problem

Maximize $z = x + y$

Subject to the constraints $x - y \leq -1$ , $x \geq y$ , $x \geq 0, y \geq 0$

Then which one of the following is TRUE?