Consider the following problem:

Minimize 5x₁ + 7x₂

Subject to:

2x₁ + x₂ 4

x₂ 6

x₁ + x₂ = 8

x_1, x₂ 0

1. Set up the initial basic feasible solution (make sure that you have a basis!), i.e., add slacks, surplus, and artificial variables to setup the model; then, do any transformation necessary so that the tableau exhibits a basic feasible solution.

2. Do one pivot using the most negative reduced cost rule and indicate the status of the problem after this pivot whether it is feasible, optimal, working toward feasibility, etc.

3. Graph this problem and state if the problem is unbounded, infeasible, or has an optimal feasible solution. If an optimal solution exists, state the solution vector and the objective function value.