With the emergence of millimeter-Wave (mmWave) communication technology, the capacity of mobile backhaul networks can be significantly increased. On the other hand, Mobile Edge Computing (MEC) provides an appropriate infrastructure to offload latency-sensitive tasks. However, the amount of resources in MEC servers is typically limited. Therefore, it is important to intelligently manage the MEC task offloading by optimizing the backhaul bandwidth and edge server resource allocation in order to decrease the overall latency of the offloaded tasks. This paper investigates the task allocation problem in MEC environment, where the mmWave technology is used in the backhaul network. We formulate a Mixed Integer NonLinear Programming (MINLP) problem with the goal to minimize the total task serving time. Its objective is to determine an optimized network topology, identify which server is used to process a given offloaded task, find the path of each user task, and determine the allocated bandwidth to each task on mmWave backhaul links. Because the problem is difficult to solve, we develop a two-step approach. First, a Mixed Integer Linear Program (MILP) determining the network topology and the routing paths is optimally solved. Then, the fractions of bandwidth allocated to each user task are optimized by solving a quasi-convex problem. Numerical results illustrate the obtained topology and routing paths for selected scenarios and show that optimizing the bandwidth allocation significantly improves the total serving time, particularly for bandwidth-intensive tasks.