Lets 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

*Maximise: *

Subject to

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:

*Maximise: *

to write has no sense.

This model needs also artificial variable.