We consider computation offloading for edge computing in a wireless network equipped with intelligent reflecting surfaces (IRSs). IRS is an emerging technology and has recently received great attention since they can improve the wireless propagation environment in a configurable manner and enhance the connections between mobile devices (MDs) and access points (APs). At this point not many papers consider edge computing in the novel context of wireless communications aided by IRS. In our studied setting, each MD offloads computation tasks to the edge server located at the AP to reduce the associated comprehensive cost, which is a weighted sum of time and energy. The edge server adjusts the IRS to maximize its earning while maintaining MDs' incentives for offloading and guaranteeing each MD a customized information rate. This problem can be formulated into a difficult optimization problem, which has a sum-of-ratio objective function as well as a bunch of nonconvex constraints. To solve this problem, we first develop an iterative evaluation procedure to identify the feasibility of the problem when confronting an arbitrary set of information rate requirement. This method serves as a sufficient condition for the problem being feasible and provides a feasible solution. Based on that we develop an algorithm to optimize the objective function. Our numerical results show that the presence of IRS enables the AP to guarantee higher information rate to all MDs and at the same time improve the earning of the edge server.