Algebra

Linear Programming

Medium

common

The minimum value of $Z = 2x + y$ subjected to $x + y \geq 10, 2x + 3y \leq 26, x, y \geq 0$ is

✅ Correct Option: 1

The objective is to minimize $Z = 2x + y$ subject to:

$x + y \geq 10$

$2x + 3y \leq 26$

$x, y \geq 0$

In linear programming, the minimum value occurs at a corner point of the feasible region.

Finding the corner points by determining where constraint lines intersect:

Where $x + y = 10$ meets $2x + 3y = 26$ :

From $x + y = 10$ :

$x = 10 - y$

Substituting into $2x + 3y = 26$ :

$2(10 - y) + 3y = 26$

$20 - 2y + 3y = 26$

$y = 6$

$x = 10 - 6 = 4$

Corner point: $(4, 6)$

Where $x + y = 10$ meets $y = 0$ :

$x + 0 = 10$

$x = 10$

Checking $2x + 3y \leq 26$ : $2(10) + 0 = 20 \leq 26$ ✓

Corner point: $(10, 0)$

Where $2x + 3y = 26$ meets $y = 0$ :

$2x + 0 = 26$

$x = 13$

Checking $x + y \geq 10$ : $13 + 0 = 13 \geq 10$ ✓

Corner point: $(13, 0)$

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

At $(4, 6)$ :

$Z = 2(4) + 6$

$Z = 8 + 6$

$Z = 14$

At $(10, 0)$ :

$Z = 2(10) + 0$

$Z = 20$

At $(13, 0)$ :

$Z = 2(13) + 0$

$Z = 26$

The minimum value of $Z$ is $14$ , occurring at the point $(4, 6)$ .

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The minimum value of Z=2x+yZ = 2x + yZ=2x+y subjected to x+y≥10,2x+3y≤26,x,y≥0x + y \geq 10, 2x + 3y \leq 26, x, y \geq 0x+y≥10,2x+3y≤26,x,y≥0 is

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CUET Mathematics Past Year Questions (Topic-Wise)

The minimum value of $Z = 2x + y$ subjected to $x + y \geq 10, 2x + 3y \leq 26, x, y \geq 0$ is