Emerging 5G services are revolutionizing the way operators manage and optimize their optical metro networks, and the metro network design process must be rethought accordingly. In particular, minimizing network cost is crucial to curb operators' investment. Taking advantage of relatively-short distances in metro networks, operators have the opportunity to optimize the placement of optical amplifiers (OAs) with the goal of minimizing amplifiers' cost (and hence decrease network cost) without significantly affecting the quality of transmitted optical signals. Minimizing OA cost translates not only in minimizing the cost of equipment (i.e., boosters, pre-amplifiers and inline amplifiers), but also in minimizing deployment and maintenance costs of active amplifier sites. In this paper, we propose a heuristic algorithm for OA placement and for the Routing and Spectrum Assignment (RSA) in metro networks, with the objective of minimizing the total cost of OAs while guaranteeing sufficient optical signal-to-noise ratio (OSNR) of established lightpaths. In our approach, we consider different cost for the deployed OAs, according to their location and type, i.e., inline amplifiers (ILAs), boosters and pre-amplifiers, and compare our optimized placement against benchmark strategies where OAs are predeployed at network nodes and at a fixed distance one from the other along optical fiber links. We also evaluate the impact of different routing strategies on the total cost and utilized spectrum. Simulative results, performed over realistic metro network topologies, show that our strategy provides up to 47% OAs cost savings while satisfying minimum OSNR constraints.