MAX 3X1 - 5X2 + 7X3

ST 2X1 + X2 - 4X3 + 2X4 > 6

-1X1 + 3X2 + 2X3 + X4 < 20

X2 +X3 - X4 = -1

X1 < 0, X2 > 0, X3 unrestricted, X4 > 0

Consider the above primal LP problem:

1. Construct the initial Simplex Table and carry on to find the optimal answer.
2. Summarize the optimal answers as follows:

X₁ = _____; X₂ = _____; X₃ = ______; X₄ = _____;

SP₁ = _____; SP₂ = ____; SP₃ = _____;

Objective Function Value of the Primal LP OVP = ______.

Where SP_i = Shadow Price associated with constraint i;

3. Formulate the dual of the above primal LP problem using Y_i as dual variables associated with the main constraints in the primal form.
4. Construct the initial Simplex Table for the dual problem and carry on to find the optimal answer of the dual LP problem.
5. Summarize the answer to the dual LP problem as follows:

Y₁ = _____; Y₂ = _____; Y₃ = ______;

SPD₁ = _____; SPD₂ = _____; SPD₃ = _____; SPD₄ = ____.

Where SPD_i = Shadow Price associated with constraint i of the dual problem;

Objective Function Value of the Dual LP OVD = ______.