Although mobile edge computing (MEC), as an extension of the cloud computing paradigm to edge networks, overcomes some obstacles of traditional mobile cloud computing, i.e., the reduced response time particularly, it is a nontrivial task to efficiently deploy virtual machine replica copies (VRCs) supporting multiple applications among numerous MEC servers in edge networks. To combat this issue, we are motivated to investigate in detail the optimal placement of VRCs to minimize the average response time (MART) in the MEC architecture with various requests demand among multiple applications and capacity constraints of MEC servers in edge networks. Besides optimal enumeration placement algorithm (OEPA) as benchmark, we design latency aware heuristic placement algorithm (LAHPA) with much lower computation complexity than that of OEPA. To enhance the performance of LAHPA on MART, clustering enhanced heuristic placement algorithm (CEHPA) is proposed, focusing on the optimal VRC placement in each cluster. We also develop substitution enhanced heuristic placement algorithm (SEHPA) to avoid falling into local optimal solutions. As corroborated by extensive simulation results, the performance of SEHPA on MART is very close to that of OEPA compared with LAHPA and CEHPA. Note that CEHPA also outperforms LAHPA, and both are better than a general greedy placement algorithm. Furthermore, we evaluate the normalized total cost for services provision in edge networks, where SEHPA can also get more outstanding results than other algorithms.