CUET UG 2025 — Mathematics Algebra

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

The constraints are:

1. $x - y \leq -1$x−y≤−1
2. $x \geq y$x≥y
3. $x \geq 0$x≥0
4. $y \geq 0$y≥0

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

$$x - y \leq -1$$x−y≤−1

$$x \leq y - 1$$x≤y−1

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

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From the second constraint:

$$x \geq y$$x≥y

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

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Comparing these two conditions:

From constraint 1: $x < y$x<y

From constraint 2: $x \geq y$x≥y

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

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Since the constraints contradict each other, no point $(x, y)$(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.