S olve the following linear optimization problem.

M aximize, Z = 2x1 + x2 S ubject to, 4x1 + 3x2 ≤ 32 x1 ≤ 5 5x1 + 6x2 ≤ 18 x1, x2 ≥ 0 U se graphical analysis to solve the above problem. Label all the corner point solutions, identify the feasible region and show clearly the profit line that runs through the optimal solution.