This paper investigates minimum mean square error (MMSE)-based amplify-and-forward (AF) relay amplifying matrices and source/destination beamforming vectors under perfectly known channel state information by imposing constraints on the transmit power of source and relays, separately and individually. The main contribution of this paper is the derivation of a set of relay amplifying matrices and source/destination beamforming vectors under transmit power constraints on the source and relay. Additionally, the SNR and the MMSE cost function behaviors will be investigated numerically and analytically.