Additional variable used in solving LP

Additional variable used in solving LP

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In practice, most problems contain more than two variables and are consequently too large to be tackled by conventional means. Therefore, an algebraic technique is used to solve large problems using Simplex Method. This method is carried out through iterative process systematically step by step, and finally the maximum or minimum values of the objective function are attained.
The basic concepts of simplex method are explained using the Example 6 of the packaging product mix problem illustrated in the previous chapter. The simplex method solves the linear programming problem in iterations to improve the value of the objective function. The simple approach not only yields the optimal solution but also other valuable information to perform economic and ‘what if’ analysis.

Additional Variables Used in Solving LPP

Three types of additional variables are used in a simplex method such as:
(a) Slack variables (S1, S2, S3..…Sn): Slack variables refer to the amount of unused resources like raw materials, labour and money.
(b) Surplus variables (-S1, -S2, -S3..…-Sn): Surplus variable is a number of resources by which the left-hand side of the equation exceeds the minimum limit.
(c) Artificial Variables (a1, a2, a3.. …an): Artificial variables are temporary slack variables which are used for purposes of calculation, and are removed later.
The above variables are used to convert the inequalities into equality equations, as given in Table 3.1 below.

Constraint Type

Variable Added

Format

(a)
Less than or equal to
Add Slack Variable
+S
(b)
Greater than or equal to
Subtract surplus variable and add artificial variable
–S + a
(c)
Equal to
=
Add artificial variable
+a