CUET UG 2025 — Mathematics Algebra

The constraints are:

$$x + y \leq 30$$x+y≤30

$$x + y \geq 15$$x+y≥15

$$y \leq 20$$y≤20

$$x \leq 15$$x≤15

$x \geq 0$x≥0 and $y \geq 0$y≥0

The corner points occur where two boundary lines intersect. The boundaries are:

$x + y = 30$x+y=30, $x + y = 15$x+y=15, $y = 20$y=20, $x = 15$x=15, $x = 0$x=0, $y = 0$y=0

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Where $x = 0$x=0 meets $x + y = 15$x+y=15:

$$0 + y = 15$$0+y=15

$$y = 15$$y=15

Point: $(0, 15)$(0,15)

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Where $x = 0$x=0 meets $y = 20$y=20:

Point: $(0, 20)$(0,20)

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Where $y = 0$y=0 meets $x + y = 15$x+y=15:

$$x + 0 = 15$$x+0=15

$$x = 15$$x=15

Point: $(15, 0)$(15,0)

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Where $x = 15$x=15 meets $x + y = 30$x+y=30:

$$15 + y = 30$$15+y=30

$$y = 15$$y=15

Point: $(15, 15)$(15,15)

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Where $y = 20$y=20 meets $x + y = 30$x+y=30:

$$x + 20 = 30$$x+20=30

$$x = 10$$x=10

Point: $(10, 20)$(10,20)

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The corner points of the feasible region are: $(15, 0)$(15,0), $(15, 15)$(15,15), $(10, 20)$(10,20), $(0, 20)$(0,20), $(0, 15)$(0,15)