Mobile cloud computing provides shared computational resources to which mobile devices can offload computational tasks in order to reduce energy consumption or reduce the latency of the task execution. The decision of whether or not to offload a task can be formulated as a joint optimization problem over the available computational and radio resources. When multiple users seek to offload tasks through a single access point, the radio resources are constrained by the region of achievable rates on the multiple access channel. In this paper a quasi-closed form solution is obtained for a problem in which two users jointly optimize their offloading decisions and their rates and power allocations so as to minimize the energy required to meet specified latency constraints.