This paper presents a mobile cloud computing application model and addresses how to minimize the energy consumption for uploading L size of data load within the T delay constraint. We propose a bandwidth allocation strategy for a LTE network with homogeneous sub-channel condition. Our objective is to allocate more bandwidth to each UE when its relative channel condition becomes better. We formulate the UE's objective function as the sum of two penalty functions: channel condition penalty function which incentivizes base stations to minimize the energy consumption for every UE and Service Level Agreement (SLA) demand penalty function which guarantees L size of data load that can be uploaded in time. In the network scenario, we formulate the EnerGy Optimized (EGO) bandwidth allocation strategy as a linear programming model and solve it by the Simplex Method. Simulation results show that EGO can save energy of up to 60% for each UE and decrease the SLA violation rate in the network of up to 30% in comparison with the existing bandwidth allocation strategy in the uplink of the LTE network.