For the following LP, identify three alternative optimal basic solutions, and then write a general expression for all the non-basic alternative optima comprising these three basic solutions.
Maximize z = x1 + 2x2 + 3x3
Subject to
X1 + 2x2 + 3x3 ≤ 10
X1 + x2 ≤ 5
X1 ≤ 0
X1, x2, x3 ≥ 0
From the optimal tableau, show that all the alternative optima are not corner points (i.e., non-basic). Give a two-dimensional graphical demonstration of the type of solution space and objective function that will produce this result. (You may use TORA for convenience.)