Macromixing in a batch bioreactor has been analysed through an extended version of a two-region model proposed earlier. Two internal dilution rates characterise the degree of macromixing. Computations for an Escherichia coli culture containing the plasmid pBR Eco gap show that in order to maximise the average concentration (or mass fraction) of plasmid-containing cells, the region into which the inoculum is introduced should be poorly (or perfectly) mixed while the other region should be perfectly (or poorly) mixed. Time-domain profiles for the two regions suggest that plasmid-containing cells become homogeneously distributed faster than plasmid-free cells. Comparison of the regional profiles for the cases of the largest average concentration and the largest-average mass fraction df plasmid-containing cells reveal differences which indicate that a partially macromixed bioreactor may be an optimal choice.