Consider an economy with a single traded asset and three possible states of the world (i.e., \(N=1\) and \(S=3\) ), with dividend \(D=(0.5,1,2)^{\top}\) and price \(p=1\). For the payoff \(c=(1,2,3)^{\top}\), determine the super-replication and sub-replication prices \(q_{u}(c)\) and \(q_{l}(c)\).