The ideas conveyed by the graphical LP solution lay the foundation for the development of the algebraic
simplex method . Figure 3.1 draws a parallel between the two methods . in the graphical method .
the solution space is delineated by the half- spaces.
simplex method . Figure 3.1 draws a parallel between the two methods . in the graphical method .
the solution space is delineated by the half- spaces.
Figure 3.1
representing the constraint and in the simplex method the solution space is represented by m simultaneous linear equations and n non-negative variable .
you will get to appreciated the meaning of the information in
Figure 3.1 as you proceed with the remainder of the section.
we can see visually why the graphical solution space has infinity of solution points, but how can we draw a similar conclusion from the algebraic representation of the solution
space?the answer is that in the algebraic representation
the number of the equations m is always less than or equal to the number of variable n.1
if m =n,and the equations are consistent .
the system has only one solution ;but if m < n
( which represents the majority of LPs ). then the system of equations again of
consistent will yield infinity of solutions .
