duality and linear programming

Question 1

duality theory:

Answer 1

the optimal value of maximise ⟨c,x⟩ subject to Ax<=b coincides with the optimal value of minimise ⟨b,y⟩ subject to A^(T)y=c, y>=0, provided they both have a finite solution
the first is called the primal problem, the second is the dual problem