The maximum value of $z = 5x + 7y$ subjected to constraints $x + y ≤ 5, x ≥ 0, y ≥ 0$ is:

35

The correct answer is Option (1) → 35

Objective function: $z = 5x + 7y$

Subject to constraints:

$x + y \leq 5$

$x \geq 0$

$y \geq 0$

Feasible region is bounded by points:

$(0, 0)$: $z = 5(0) + 7(0) = 0$

$(5, 0)$: $z = 5(5) + 7(0) = 25$

$(0, 5)$: $z = 5(0) + 7(5) = 35$

Maximum value of $z$ is $35$ at point $(0, 5)$