Problems:
Duality, Complementary Slackness, Dual Simplex Algorithm and Feasibility
Consider the linear program:
Min -2x-y
St x-y<2
x+y<6
x, y> 0
a) By inspection, argue that this problem cannot have an unbounded optimal solution.
b) Convert this problem to simplex standard form, enumerate all the basic solutions, identify which ones are feasible, and compute their objective values.
c) What is the optimal solution to this problem? How do you know?
d) What is the dual of this problem?
e) Use complementary slackness to prove your answer in part c.
f) For each basis in part b, use complementary slackness to find the corresponding basic solution to the dual problem, identify whether it's feasible, and compute its objective value.
g) Select a basis from part b which is primal infeasible but dual feasible. Using this as your initial solution, compute ONE pivot of the dual simplex algorithm. Is your new solution optimal? Why or why not?