Consider the following LP problem:
min x_{1 }+3_{x2 }+x_{3} -x_{4}
s.t. x_{1} +x_{2} +x_{3} +x_{4} ≥ 0
x_{1} +x_{2} -x_{3} -x_{4} ≥ 1
x_{2}, x_{3} ≥ 0 x_{1}, x_{4} ≤ 0.
1. Unique primal-dual solutions.