I analyse the solution method for the variational optimisation problem in the rational inattention framework proposed by Christopher A. Sims. The solution, in general, does not exist, although it may exist in exceptional cases. I show that the solution does not exist for the quadratic and the logarithmic objective functions analysed by Sims (2003, 2006). For a linear-quadratic objective function a solution can be constructed under restrictions on all but one of its parameters. This approach is, therefore, unlikely to be applicable to a wider set of economic models.