Recently, adopting mobile-edge computing (MEC) to accommodate the compute-intensive and delay-sensitive tasks from mobile devices has gained increasing attention from the research community. In contrast to a cloud-centric scheme, deploying servers at the network edge offers the advantage of delivering faster and more efficient services. However, pioneering works primarily focus on a homogeneous server deployment strategy, which distributes the same quantity of servers among a specific number of selected locations. In this work, we aim to lay the theoretical foundation for budget-constrained profits maximization (BCPM) problem, which is a coupled problem of server deployment and task scheduling. Subsequently, a two-step optimization method is proposed. Through seeking the maximum matches in the constructed bipartite graph, a task scheduling algorithm is first designed to maximize the profits under the server deployment. Then, two approximation algorithms with provable approximation ratios are exploited to perform nearly optimal deployment of servers in a homogeneous and heterogeneous manner, respectively. Extensive simulations with real-world data set and system settings are conducted. The results show that the proposed algorithms can achieve at least a 10.54% increase in total profits and the average processing delay of tasks can be shortened by about 17%.