We develop a model to estimate the production cross section of heavy tetraquarks as a function of the center of mass energy. The model employs two formalisms, namely the Double Parton Scattering (DPS) processes and the Color Evaporation Model (CEM). In a previous work we used our model to estimate the production cross section of the X(3872) and of the T$_{4c}$ in proton-proton collisions at the LHC. Now we employ it to estimate the production cross section of the T$_{4b}$, a tetraquark composed by two $b\bar{b}$ pairs, and of the T$_{2bc}$, a tetraquark composed by a $b\bar{b}$ and a $c\bar{c}$, at the energies of the LHC.