Mobile Edge Computing (MEC) offloads service functionalities from central cloud to edge network and process user requests there, which reduces service latency and alleviates cloud burden. Only partial services can run on edge nodes with limited resource capacity. Both time varying and heterogeneity of services users requesting introduce great challenges for the resource utilization of edge nodes and user quality of service (QoS). Edge cooperation with joint optimization emerges to cope with this problem for MEC service provider. Recent researches focus on the non-cooperation or partial cooperation among edge nodes in local area network (LAN), their benefits are only explored on a small scale, and the users still face with resources waste and high service. This paper jointly optimizes service placing and task scheduling in MEC based on edge utility maximization and full cooperation of edge nodes in LAN. Edge full cooperation can place as many types of services as possible and capture more user requests in edge network so as to reduce the overall delay and edge energy consumption. Further considering the individual user QoS, we formularize the rewards in the edge utility to promote the local processing of user tasks. The joint optimization is a mixed integer nonlinear program problem which is NP-hard with high computational complexity. Therefore, we design a two-layer iterative strategy (TI-ST) based on Gibbs sampling and linear programming, which has polynomial computation complexity and has provably near optimal performance. Experimental results demonstrate the effectiveness of the proposed scheme when compared with the benchmark schemes.