  We propose and analyze a new class of controlled multi-type branching
processes with a per-step linear resource constraint, motivated by potential
applications in viral marketing and cancer treatment. We show that the optimal
exponential growth rate of the population can be achieved by maintaining a
fixed proportion among the species, for both deterministic and stochastic
branching processes. In the special case of a two-type population and with a
symmetric reward structure, the optimal proportion is obtained in closed-form.
  In addition to revealing structural properties of controlled branching
processes, our results are intended to provide the practitioners with an
easy-to-interpret benchmark for best practices, if not exact policies. As a
proof of concept, the methodology is applied to the linkage structure of the
2004 US Presidential Election blogosphere, where the optimal growth rate
demonstrates sizable gains over a uniform selection strategy, and to a
two-compartment cell-cycle kinetics model for cancer growth, with realistic
parameters, where the robust estimate for minimal treatment intensity under a
worst-case growth rate is noticeably more conservative compared to that
obtained using more optimistic assumptions.
