For a hypergraph and k different colors, we study the problem of packing and coloring some hyperedges of the hypergraph as paths in a cycle such that the total profit of the chosen hyperedges are maximized, here each link ej on the cycle is used at most cj times, each hyperedge hi has a profit pi and any two paths, each spanning all vertices of its corresponding hyperedge, must receive different colors if they share a link. This new problem arises in optical communication networks and it is called the Maximum Profits of Packing and Coloring Hyperedges in a Cycle problem MPPCHC. Ini¾?this paper, we prove that the MPPCHC problem is NP-hard and present a 2-approximation algorithm. For the special case, where each hyperedge has the same profit and each capacity cj is k, we propose a $\frac{3}{2}$ -approximation algorithm to handle the problem. AMS Classifications: 90B10, 94C15.