In this paper we consider the problem of selecting assets for which transaction costs are given by piecewise affine functions. Given practical constraints related to budget and buy-in thresholds, our purpose is to determine the number of each asset i that can produce the maximum return of a portfolio composed of (n + 1) assets (one of them is free of risk). The problem is formulated as an integer quadratic problem and afterwards linearized. Some numerical experiments, using Ilog Cplex 10.1, has been performed. They show that the methodology is promising.