In this paper, we study power allocation strategies for a fixed-gain amplify-and-forward relay network employing multiple relays. We consider two optimization problems for the relay network: 1) maximizing the end-to-end signal-to-noise ratio (SNR) and 2) minimizing the total power consumption while maintaining the end-to-end SNR over a threshold value. We investigate these two problems for two relaying protocols of all-participate (AP) relaying and selective relaying and two cases of feedback to the relays, namely full and limited. We show that the SNR maximization problem is concave and that the power minimization problem is convex for all protocols and feedback cases considered. We obtain closed-form expressions for the two problems in the case of full feedback and solve the problems through convex programming for limited feedback. Numerical results show the benefit of having full feedback at the relays for both optimization problems. However, they also show that feedback overhead can be reduced by having only limited feedback to the relays with only a small degradation in performance.