a) Infeasible when α, β∈R
Because none of these values satisfied the equation at first.
b) Has an optimal when both α,β >0 and α≠β
Because if α>β the unique optimal will at x1=1/β, while when β >α the unique optimal
will at x2=1/α. When α=β the optimal solution is at x1+x2= 1/α.
c) Feasible and unbounded when α>=0
we can increase x without violating any constraint. The same stands true for β>=0
and increase in y. When both α and β are positive, the conditions satisfy for all
values of α and β.
d) Has multiple optimal solutions when α=β
Because it can satisfy multiple values of x1 and x2.