Solve the following LP using Simplex method.
Maximize x1 + x2 + x3
S.T. x1 +4x2 +4x3 ?8
2x1 + x2 + x3 ? 4 x1,x2,x3 ?0
(a) First convert the LP into standard form.
(b) Start at the BFS (Basic Feasible Solution) in which x1,x2 and x3 are nonbasic variables.
(c) At each pivoting operation increase the nonbasic variable with the largest reduced cost coefficient from zero. The nonbasic variable you choose is also said to enter the basis.
(d) If you have a choice of several basic variables that you can move out of the basis, pick the one with the smallest subscript.
(e) Show all of the calculations in each pivoting operation. That is, you need to show the calculations underlying the checks for unboundedness and optimality.
(f) For each pivoting operation show the corresponding transition between the ver- tices of the underlying polyhedron. (You drew the polyhedron corresponding to this LP in Homework 4.)