CUET UG 2025 — Mathematics Algebra

We need to find the corner points of the feasible region and add up their $x$x-coordinates.

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The constraints are:

$$x + y \leq 14$$x+y≤14

$$x \geq 4$$x≥4

$$x \leq 8$$x≤8

$$y \geq 0$$y≥0

The corner points occur where these boundary lines intersect.

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Where $x = 4$x=4 meets $y = 0$y=0:

Point: $(4, 0)$(4,0)

$x$x-coordinate $= 4$=4

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Where $x = 4$x=4 meets $x + y = 14$x+y=14:

Substituting $x = 4$x=4:

$$4 + y = 14$$4+y=14

$$y = 10$$y=10

Point: $(4, 10)$(4,10)

$x$x-coordinate $= 4$=4

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Where $x = 8$x=8 meets $x + y = 14$x+y=14:

Substituting $x = 8$x=8:

$$8 + y = 14$$8+y=14

$$y = 6$$y=6

Point: $(8, 6)$(8,6)

$x$x-coordinate $= 8$=8

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Where $x = 8$x=8 meets $y = 0$y=0:

Point: $(8, 0)$(8,0)

$x$x-coordinate $= 8$=8

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Sum of $x$x-coordinates:

$$4 + 4 + 8 + 8 = 24$$4+4+8+8=24

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Answer: $24$24