Final answer:
This problem is related to integer programming. To solve it, you can use the branch and bound method to systematically explore and find the optimal solution for the objective function z, while satisfying all the constraints.
Step-by-step explanation:
This problem is related to integer programming. Integer programming is a mathematical optimization technique where the variables are restricted to integers. In this case, we have the objective function z = x₁ + 2x₂, and three constraints: -3x₁ + 4x₂ ≤ 4, 3x₁ + 2x₂ ≤ 11, and 2x₁ - x₂ ≤ 5.
To solve this problem, you can use the branch and bound method. This method involves creating a tree and systematically exploring the different possible values for the variables. At each node, you compute the objective function value and check if it is better than the current best solution.
By solving the problem using branch and bound, you can find the optimal solution for the objective function z, while satisfying all the constraints.