Resource Allocation (RA) is one of the crucial elements in Long Term Evolution (LTE) networks, which has a tremendous impact on the network performance. However, complexity of the RA problem increases when both Carrier Aggregation (CA) and Multiple-Input Multiple-Output (MIMO) are enabled in the network. CA is a key functionality for LTE-Advanced (LTE-A) that enables Mobile Network Operators (MNOs) to create large virtual carrier bandwidths for data hungry applications by aggregating available Component Carriers (CCs). In this paper, Resource Block (RB), Secondary CC (SCC), MIMO Transmission Mode (TM), and Modulation and Coding Scheme (MCS) selection is formulated jointly as an Integer Linear Programming (ILP). We prove that intractable integrality of the optimisation problem can be removed and relaxed to the Linear Programming (LP). Solving the LP obtains an optimal solution for the original ILP. © 2016 IEEE.