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 answer as follows:

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

SP1 = _____; SP2 = ____; SP3 = _____;

Objective Function Value of the Primal LP OVP = ______.

Where SPi = Shadow Price associated with constraint i;

3. Formulate the dual of the above primal LP problem.

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 SPDi = Shadow Price associated with constraint i;

Objective Function Value of the Dual LP OVD = ______.

6. State a general conclusion about the primal and the dual LP.