4 min z = 3x1 s.t. 2x1 + x2 2 6 3x1 + 2x2 = 4 X1, X2 2 0
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Use the Big M method to solve the following LPs:
The given LPP problem,
Subject to the constraints,
Using the Big M method to solve the LPP.
The given LPP problem,
Subject to the constraints,
The problem is converted into canonical form by adding slack, surplus, and artificial variables as appropriate.
1. As the constraint- is of type we should subtract the surplus variable and add the artificial variable .
2. As the constraint- is of type we should add the artificial variable .
After introducing surplus, artificial variables.
Subject to the constraints,
First iteration:
| Iteration-1 | 3 | 0 | 0 | M | M | |||
| B |
Min Ratio |
|||||||
| M | 6 | 2 | 1 | -1 | 1 | 0 | ||
| M | 4 | 3 | 2 | 0 | 0 | 1 | ||
| 5M | 3M | -M | M | M | ||||
| 5M-3 | 3M | -M | 0 | 0 |
Positive maximum is . So the entering variable is .
Minimum ratio is . So the leaving basis variable is .
Therefore the pivot element is .
Step by step
Solved in 5 steps
