This is a linear programming problem where the objective is to maximize $Z = 5x_1 + 25x_2$, subject to the given constraints:

Problem formulation:

1. Objective function: $\text{Maximize } Z = 5x_1 + 25x_2$

2. Subject to: $-x_1 + x_2 \geq 0 \quad \text{(or equivalently, } x_2 \geq x_1\text{)}$ $x_1 + x_2 \leq 5$ $-2x_1 + x_2 \leq 16$ $x_1 \geq 0, \quad x_2 \geq 0$

Would you like me to solve this problem using graphical methods or optimization techniques such as the simplex method? Let me know how you'd like to proceed!

Here are five follow-up questions based on this problem:

1. Would you like an explanation of how the feasible region is determined for the constraints?
2. Should I rewrite the constraints into slope-intercept form for better visualization?
3. Would you like me to identify all the corner points of the feasible region?
4. Do you need help plotting this problem graphically step-by-step?
5. Should I solve this problem step-by-step using the simplex method?

Tip: In linear programming, always verify whether the constraints form a bounded feasible region; this ensures a solution exists!