Cooperation between the fog and the cloud in mobile cloud computing environments could offer improved offloading services to smart mobile user equipment (UE) with computation intensive tasks. In this paper, we tackle the computation offloading problem in a mixed fog/cloud system by jointly optimizing the offloading decisions and the allocation of computation resource, transmit power, and radio bandwidth while guaranteeing user fairness and maximum tolerable delay. This optimization problem is formulated to minimize the maximal weighted cost of delay and energy consumption (EC) among all UEs, which is a mixed-integer non-linear programming problem. Due to the NP-hardness of the problem, we propose a low-complexity suboptimal algorithm to solve it, where the offloading decisions are obtained via semidefinite relaxation and randomization, and the resource allocation is obtained using fractional programming theory and Lagrangian dual decomposition. Simulation results are presented to verify the convergence performance of our proposed algorithms and their achieved fairness among UEs, and the performance gains in terms of delay, EC, and the number of beneficial UEs over existing algorithms.