linear programming problem

Linear programming problem below, state the dual problem, solve by the simplex or dual simplex method & also states the solutions to both problems.

1. Maximize x1 − 2x2 − 3x3 − x4 subject to the constraints xj ≥ 0 for all j and

x1 − x2 − 2x3 − x4 ≤ 4

2x1 + x3 − 4x4 ≤ 2

−2x1 + x2 + x4 ≤ 1.

2. Minimize 3y1 − y2 + 2y3 subject to the constraints yi ≥ 0 for all i and

2y1 − y2 + y3 ≥ −1

y1 + 2y3 ≥ 2

−7y1 + 4y2 − 6y3 ≥ 1.

3. Maximize −x1 − x2 + 2x3 subject to the constraints xj ≥ 0 for all j and

−3x1 + 3x2 + x3 ≤ 3

2x1 − x2 − 2x3 ≤ 1

−x1 + x3 ≤ 1.

4. Minimize 5y1 − 2y2 − y3 subject to the constraints yi ≥ 0 for all i and

−2y1 + 3y3 ≥ −1

2y1 − y2 + y3 ≥ 1

3y1 + 2y2 − y3 ≥ 0.

5. Minimize −2y2 + y3 subject to the constraints yi ≥ 0 for all i and

−y1 − 2y2 ≥ −3

4y1 + y2 + 7y3 ≥ −1

2y1 − 3y2 + y3 ≥ −5.

6. Maximize 3x1 + 4x2 + 5x3 subject to the constraints xj ≥ 0 for all j and

X1 + 2x2 + 2x3 ≤ 1

−3x1 + x3 ≤ −1

−2x1 − x2 ≤ −1.

In our next blog we shall learn about list of ionic compounds I hope the above explanation was useful.Keep reading and leave your comments.