This is a linear programming problem that involves maximizing an objective function $f = x_1 + 3x_2$ under several constraints. Let's rewrite the problem clearly:

Objective Function:

$f = x_1 + 3x_2 \quad \rightarrow \text{max}$

Constraints:

1. $x_1 + x_2 \leq 3$
2. $6x_1 + x_2 \geq 4$
3. $2x_1 - 3x_2 \geq 6$
4. $x_1 \geq 0$ (non-negativity)
5. $x_2 \geq 0$ (non-negativity)

The solution involves:

1. Graphing the feasible region formed by these constraints.
2. Identifying the vertices of the feasible region.
3. Substituting the coordinates of the vertices into the objective function $f = x_1 + 3x_2$ to determine the maximum value.

Steps for Solving the Problem:

1. Graph the Constraints: Convert inequalities into equations to find boundaries:
   • (