Final answer:
To maximize the given objective function, we need to use linear programming techniques and solve for the optimal solution.
Step-by-step explanation:
The given problem is a linear programming problem, which involves maximizing an objective function subject to a set of constraints. In this case, the objective function is z = 5x1 + 12x2 and we want to maximize it. The variables x1 and x2 represent decision variables that we can adjust.
The problem also provides constraints and additional information, but they are not specified in the question. To solve this problem, we would need the constraints to determine the feasible region and find the optimal solution. Typically, we use graphical methods (plotting the constraints and objective function on a graph) or matrix methods (solving the problem using linear algebra) to find the optimal solution.