The given Linear Programming Problem (LPP) is structured as follows:

Objective Function:

Maximize $Z = 12x_1 + 16x_2$

Subject to the constraints:

1. $10x_1 + 20x_2 \leq 120$
2. $8x_1 + 8x_2 \leq 80$
3. $x_1 \geq 0, x_2 \geq 0$ (non-negativity constraints)

Steps to solve this LPP:

1. Plot the constraints: Convert the inequalities into equalities to find the boundary lines.
2. Find the feasible region: This is the region where all the constraints overlap.
3. Identify the corner points: These are points where the boundary lines intersect.
4. Evaluate the objective function at each corner point: Compute the value of $Z$ at each of these points.
5. Find the maximum value of $Z$: The corner point giving the highest $Z$ is the solution.

Would you like me to proceed with plotting the constraints and solving it step-by-step?

Here are 5 related questions for further exploration:

1. How do we find the corner points in a feasible region?
2. What is the graphical method for solving a linear programming problem?
3. Can you explain the simplex method for solving LPPs?
4. What is the difference between bounded and unbounded feasible regions?
5. How do we solve LPPs with more than two variables?

Tip: Always check whether the feasible region is bounded, as this guarantees a maximum or minimum solution for the objective function.