Let’s reformulate the modelExample: Product processing – LP model in order to be able to formulate the initial basic solution:

… number of units of product A to be produced

… number of units of product B to be produced

… number of units of product C to be produced

… number of units of product D to be produced

P … total profit

Subject to

We add slack variables (positive) and surplus variable (negative) as follows:

x_{5 . . .} not used milling time

x_{6 . . .} not used assembly time

x_{7 . . .} not used finances for production costs

x_{8 . . .} reserve to maximal possible production of A

x_{9 . . .} reserve to maximal possible production of C

x_{10 . . .} surplus to minimal possible production of d

Since the slack and surplus variables have zero coefficients in the objective function, the objective function remains the same:

to write has no sense.

This model needs also artificial variable.