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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.)

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.)

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