For both fundamental biology and engineering applications, it is relevant to investigate how microorganisms adapt to changing environmental conditions. In this work, we consider a continuous-time dynamic problem of resource allocation between metabolic and gene expression machineries for a self-replicating prokaryotic cell population. In compliance with evolutionary principles, the criterion is to maximize the accumulated structural biomass. In the model, we include both degradation of proteins into amino acids and recycling of the latter (i. e., using as precursors again). Based on the analytical investigation of our problem by Pontryagin's maximum principle, we develop a numerical algorithm for approximating the switching curve of the optimal feedback control strategy. The obtained field of extremal state trajectories consists of chattering arcs and one steady-state singular arc. The constructed feedback control law can serve as a benchmark for comparing actual bacterial strategies of resource allocation. We also study the influence of temperature, whose increase intensifies protein degradation. While the growth rate suddenly decreases with the increase of temperature in a certain range, the optimal control synthesis appears to be essentially less sensitive.