The paper examines the problem of rational choice by a population of a patch containing energy (food) resources. This problem belongs to the theory of optimal foraging, which studies issues related to the behavior of a population leaving a patch or choosing the most suitable one. We used an approach based on the idea of the Boltzmann distribution to determine the optimal choice of a patch: in statistical physics, the Boltzmann distribution describes the probability of a system falling into a particular energy state. In this paper, the Boltzmann distribution is constructed taking into account the utility functions, which, in turn, are derived taking into account the population’s awareness of the quality of patches, the volume of energy resources in each patch, and the costs of obtaining information (total information cost) about patch quality. Also, a non-negative parameter that characterizes the rationality of the population’s choice of patchis taken into account. At the same time, this parameter influences on the cost of information. We introduce the concept of optimal rationality, which is determined taking into account the cost of information and the energy value of all patches. The goal of this paper is to elaborate the proposed approach to address the problem of the optimal patch choice by a population. Patches are divided into two types: “bad” and “good”, depending on the volume of food resources they contain. The volume of food resources in the patches varies over time. The results of the study are general in nature and can be used in constructing various decision-making processes.