We study a two-hop multiple access channel (MAC), where two source nodes communicate with the destination node via a set of amplify-and-forward (AF) relays. To characterize the optimal rate region, we focus on deriving the boundary points of it, which is formulated as a weighted sum rate maximization problem. In the first part, we are concerned with the scenario that all relays are under a sum power constraint. Although the optimal AF rate region for the case has been obtained, we revisit the results by an alternative method. The first step is to investigate the algebraic structures of the three SNR functions in the rate set of the two-hop MAC with a specific AF scheme. Then an equivalent optimization problem is established for deriving each boundary point of the optimal rate region. From the geometric perspective, the problem has a simple solution by optimizing a one-dimensional problem
constraint. In the second part, the optimal rate region of a two-hop MAC under the individual power constraints is discussed, which is still an open problem. An algorithm is proposed to compute the maximum individual and sum rates along with the corresponding AF schemes.