For an LPP: Maximize z = 3x+9y ;x ≥0,y≥0, the feasible region OAB is…

The correct answer is Option (4) → $x + 3y ≤ 60,x ≤ y$

$\textbf{Given:}$

Maximize $z = 3x + 9y$ with $x \ge 0,\; y \ge 0$.

The shaded feasible region $OAB$ is shown in the figure.

$\textbf{From the graph:}$

Line passing through $(60,0)$ and $(0,20)$ is

$x + 3y = 60$

The feasible region lies \emph{below} this line, hence

$x + 3y \le 60$

The other boundary line shown is $x = y$.

The feasible region lies on the side where $x$ is less than or equal to $y$, hence

$x \le y$

$\textbf{Therefore, the other constraints are:}$

$x + 3y \le 60,\; x \le y$

Final Answer: The other constraints are $x + 3y \le 60$ and $x \le y$.