This work investigates the entropy production rate, Pi, of the run-and-tumble model with a focus on scaling of Pi as a function of the persistence time tau. It is determined that (i) Pi vanishes in the limit tau -> infinity, marking it as an equilibrium. Stationary distributions in this limit are represented by a superposition of Boltzmann functions in analogy to a system with quenched disorder. (ii) Optimal Pi is attained in the limit tau -> 0, marking it as a system maximally removed from equilibrium. Paradoxically, the stationary distributions in this limit have the Boltzmann form. The value of Pi in this limit is that of an unconfined run-and-tumble particle and is related to the dissipation energy of a sedimenting particle. In addition to these general conclusions, this work derives an exact expression of Pi for the run-and-tumble particles in a harmonic trap.