3. Consider the following LP problem, in which slack variables have already been inserted: maximise 3x + x2 xX3…

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3. Consider the following LP problem, in which slack variables have already been inserted:

maximise 3x₁ + x2 xX3

subject to

2

+x5

5

X1, X2, X3, X4, X5 ≥ 0

2×1 + 2×2

-x₁ − 3x₂ + 2×3

x3 + x4

That is, maximise c¹x s.t. Ax = b and x ≥ 0.

=

(a) For the basis x2, x3 (in that order) identify and write the basis matrix B, and verify

that its inverse B-1

[3₂2]

(b) Calculate B-¹b and hence write the basic solution corresponding to the basis x2, X3.

Is it a feasible solution?

(c) Identify and write the basic cost vector c. Calculate the row vector (c3B-¹)A – ct

and hence explain why this basic solution is not optimal.

(d) Explain why x₁ is a candidate to enter the basis. Calculate the column B¯¹P₁ where

P₁ is the ₁ column of the original matrix A. Use an appropriate ratio test to determine

which basic variable would leave the basis.

There is no need to execute any more calculations beyond determining which variable

leaves the basis.

Expert Answer:

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Given equations 3x x x subject to 2x 2x x x 2 x 3x 2x x 5 x x x x x 0 a To identify the basis matrix

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