4 Consider the following problem max 3x1 2x2 x3 x4 s t 2x1 3x...

4-Consider the following problem: max âˆ’ 3x1 + 2x2 âˆ’ x3 + x4 s.t. 2x1 âˆ’ 3x2 âˆ’...

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Advance Math

4-Consider the following problem:
max âˆ’ 3x1 + 2x2 âˆ’ x3 + x4
s.t.
2x1 âˆ’ 3x2 âˆ’ x3 + x4 â‰¤ 0
âˆ’ x1 + 2x2 + 2x3 âˆ’ 3x4 â‰¤ 1
âˆ’ x1 + x2 âˆ’ 4x3 + x4 â‰¤ 8
x1, x2, x3, x4 â‰¥ 0
Use the Simplex method to verify that the optimal objectivevalue is unbounded. Make use of the final tableau to construct anunbounded direction..

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Solution Problem is Max Z 3 x1 2 x2 x3 x4 subject to 2 x1 3 x2 x3 x4 0 x1 2 x2 2 x3 3 x4 1 x1 x2 4 x3 x4 8 and x1x2x3x40 The problem is converted to canonical form by adding slack surplus and artificial variables as appropiate 1 As the constraint1 is of type we should add slack variable S1 2 As the constraint2 is of type we should add slack variable S2 3 As the constraint3 See Answer

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