a$)$ If b $>0$ and c $>0,$ then the primal problem $($the maximization problem$)$ is unbounded

and the dual problem is infeasible.

b$)$ If b $>0$ and c $<0,$ then both primal and dual problem have an optimal solution.

c$)$ If b $<0$ and c $>0,$ then both primal and dual problems are infeasible.

d$)$ If b $<0$ and c $<0,$ then the primal is infeasible and the dual is unbounded.