The maximum value of $z = 5x + 7y$ subjected to constraints $x + y ≤ 5, x ≥ 0, y ≥ 0$ is:
Answer & explanation
Correct answer: option 1
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 $(0, 5)$