Showing posts with label linear programming problem. Show all posts
Showing posts with label linear programming problem. Show all posts

Friday, September 3

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.