Consider the following problem.

Maximize Z  4x1  5x2  3x3, subject to x1  x2  2x3  20 15x1  6x2 5x3 50 x1  3x2  5x3 30 and x1  0, x2  0, x3  0.

Work through the simplex method step by step to demonstrate that this problem does not possess any feasible solutions.