(Operation Research II Industrial Engineering)
Consider the following LP:
Minimize z = x1 + 2x2
Subject to x1 + x2 >= 1
-x1 + 2x2 <= 3
x2 <= 5
x1,x2 >= 0
(a) Convert the LP given above to the standard form. Determineall the basic feasible solutions (bfs) of the problem. Give thevalues of both basic and nonbasic variables in each bfs.
(b) Identify the adjacent basic feasible solutions of eachextreme point of the feasible region. Using the graphical solutiontechnique, solve the problem. Which constraints are active(binding) in the optimal solution? Which constraint(s) is(are)redundant?
(c) To have alternative optimal solutions on the firstconstraint, what should be the objective function coefficient ofthe variable x1?
(d) Using the big-M simplex method, solve the LP where theconstraint -x1 + 2x2 <= 3 is replaced by-x1 +2x2 = 3.
(e) Using the two phase method, solve the LP.
