The shared computational resources provided by the mobile cloud computing paradigm offer the opportunity for mobile devices to reduce the energy expended, or the latency incurred, in performing significant computational tasks. To maximize their impact, cloud computing systems must jointly optimize the allocation of the computational and radio resources. We consider a scenario in which two mobile users access a finite computational resource through a single wireless access point. The resources to be allocated are the fractions of the computational resource allocated to each user, and the users' transmission powers and data rates. The key constraints are the size of the computational resource and the region of rates that can be achieved by the chosen multiple access scheme. In this paper a quasi-closed-form solution is obtained to a problem in which the computational fractions, powers and rates are optimized so as to minimize the energy required to offload tasks with specified latency constraints. In doing so, it is shown that by exploiting the fundamental capabilities of the multiple access channel, rather than just the rates of a particular multiple access scheme, the energy required to offload the tasks can be substantially reduced.