This image represents the same linear programming problem. To recap:

Problem Summary:

Objective Function: $z = x_1 + 5x_2 \to \text{maximize.}$

Constraints:

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

Steps for Solution:

1. Rewrite the constraints for graphing:
   • $x_1 + x_2 \geq 3 \implies x_1 + x_2 = 3$ (boundary line, shading above).
   • $x_1 - 2x_2 \leq 0 \implies x_1 - 2x_2 = 0$ (boundary line, shading below).
   • $2x_1 - x_2 \geq 0 \implies 2x_1 - x_2 = 0$ (boundary line, shading above).
2. Identify the feasible region by