AMS 540 / MBA 540 (Fall, 2010)Estie ArkinHomework Set # 3: Solution notes1).(a). State a non degenerate BFS for the following LP: (make sure to say which variables arebasic, which are non basic and what is variable is equal to.)maxz= 6x1+ 4x2+x3s.t.x1+x2+x3≤1x1≤1x1, x2, x3≥0Introduce slack variabless1,s2in the first and second constraints to get standard form (remem-ber that Basic Solutions are defined only for standard form).maxz= 6x1+ 4x2+x3s.t.x1+x2+x3+s1= 1x1+s2= 1x1, x2, x3, s1, s2≥0Let a BFS bes1=s2= 1 basic variables (non degenerate) andx1=x2=x3= 0 non basic.(Recall, the number of basic variables must bem, the number of constraints, which is 2 in ourcase.)(b). State a degenerate BFS for the LP in part (a). Basic variablesx1= 1 andx2= 0 (degenerate),x3=s1=s2= 0 non basic.2).(a). The current BFS is optimal.c1≤0,c2≤0, (optimality)b≥0 (feasible).(b). The current basic solution is not feasible.b <0.
This is the end of the preview.
access the rest of the document.