We studied a class of Service Overlay Network (SON) design problem with reliability constraints. It is assumed that a SON network could enter an inadmissible status for two reasons; first when there is insufficient resource to accommodate new connections, second when some hardware devices malfunction. The design problem is usually formulated as either a Maximum Profit (MP) constrained optimization problem or a Minimum Cost (MC) constrained optimization problem. In this article we investigate the relationship between the two formulations in the context of ensuring system operability. By using the set of Lagrange multipliers from the MC formulation as a tool, we show the general condition that MP and MC give exactly the same network designs. The key contribution of this paper is the provision of insight into the solution nature of the MP and the MC formulations in designing a reliable overlay network, thereby giving guidelines to the proper formulation the network designers may consider in designing a reliable yet economically optimal SON network.