# Additional variable used in solving LP

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### Additional Variables Used in Solving LPP

##### The above variables are used to convert the inequalities into equality equations, as given in the Table 3.1 below.

Table 3.1: Types of Additional Variables

### Maximization Case

##### Though there are many forms of presenting Simplex Table for calculation, we represent the coefficients of variables in a tabular form as shown in Table 3.2.

Table 3.2: Co-efficients of Variables

##### If the objective of the given problem is a maximization one, enter the co-efficient of the objective function Zj with opposite sign as shown in Table 3.3. Take the most negative coefficient of the objective function and that is the key column K c. In this case, it is -6. Find the ratio between the solution value and the key column coefficient and enter it in the minimum ratio column. The intersecting coefficients of the key column and key row are called the pivotal element i.e. 2. The variable corresponding to the key column is the entering element of the next iteration table and the corresponding variable of the key row is the leaving element of the next iteration table. In other words, x1 replaces S4 in the next iteration table. Table 3.3 indicates the key column, key row and the pivotal element.

Table 3.3

1 30
##### = 6(15) + 4(30)

Table 3.5: Iteration 2