Suppose that the three-variable linear programming problem given in Fig. 5.2 has the objective function
Maximize Z = 3x1 + 4x2 + 3x3.

Without using the algebra of the simplex method, apply just its geometric reasoning (including choosing the edge giving the maximum rate of increase of Z) to determine and explain the path it would follow in Fig. 5.2 from the origin to the optimal solution.