Algebra

Linear Programming

Medium

core

The maximum value of the objective function $Z = 2x + y$ of an LPP, subject to the constraints $x \leq 6, y \leq 2, x - y \leq 0$ , $x \geq 0, y \geq 0$ is

✅ Correct Option: 2

The constraints are:

$x \leq 6$

$y \leq 2$

$x - y \leq 0$ (which means $x \leq y$ )

$x \geq 0$

$y \geq 0$

In Linear Programming, the maximum or minimum value occurs at a corner point of the feasible region.

The corner points are found by checking where the boundary lines intersect:

Origin: $(0, 0)$

Where $x = 0$ meets $y = 2$ : $(0, 2)$

Where $x = y$ meets $y = 2$ :

If $y = 2$ and $x = y$ , then $x = 2$

Point: $(2, 2)$

Note: The constraint $x \leq 6$ is not active since $x \leq y$ and $y \leq 2$ means $x$ cannot exceed $2$ .

Evaluating $Z = 2x + y$ at each corner point:

At $(0, 0)$ :

$Z = 2(0) + 0 = 0$

At $(0, 2)$ :

$Z = 2(0) + 2 = 2$

At $(2, 2)$ :

$Z = 2(2) + 2$

$Z = 4 + 2$

$Z = 6$

Comparing all values: $0$ , $2$ , and $6$

The maximum value is $6$ at point $(2, 2)$ .

2025: 21 May Shift 2

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Which of the following is NOT correct?

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$3x+y \leq 12$

$x+2y \leq 10$

$x \geq 0, y \geq 0$

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The feasible region for an LPP is shown in the given figure. Let $Z=3x+4y$ be the objective function. Then which of the following is/are TRUE?

(A) The minimum value of Z is 156

(B) The minimum value of Z is 152

(D) Neither minimum nor maximum value of Z exists

Choose the correct answer from the options given below:

The maximum value of the objective function Z=2x+yZ = 2x + yZ=2x+y of an LPP, subject to the constraints x≤6,y≤2,x−y≤0x \leq 6, y \leq 2, x - y \leq 0x≤6,y≤2,x−y≤0, x≥0,y≥0x \geq 0, y \geq 0x≥0,y≥0 is

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CUET Mathematics Past Year Questions (Topic-Wise)

The maximum value of the objective function $Z = 2x + y$ of an LPP, subject to the constraints $x \leq 6, y \leq 2, x - y \leq 0$ , $x \geq 0, y \geq 0$ is