simplex method I

The simplex method computations are particularly tedious and repetitive. It attempts to move from one corner point of the solution space to a better corner point until the optimum is found.The simplex method computation is imposing two requirements on the constrains of the problem all constraints (with the exception of the nonnegative of the variable) are equations with nonnegative right-hand side and all the variables are nonnegative. convert inequalities into equation with nonnegative right-hand side. in the graphical method, the solution space is delineated by the half-space representing the constraints, and in the simplex method the solution space is represented by m simultaneous linear equations and n nonnegative variables.The graphical solution space has an infinite number of solution points, but how can we draw a similar conclusion from the algebraic representation of the solution space.the simplex method investigates only a "select few" of these solutions. the simplex method starts at the origin (point A) where x1=0 and x2=0. At
this starting point, the value of the objective function, z, is zero, and the logical question is whether an increase in nonbasic x1 and/or x2 above their current zero values can improve (increase) the value of z. We answer this question by investigating the objective function: