Abstract
In this paper, a nonlinear dynamical controlled system of differential equations describing the process of production and sales of a perishable consumer good is studied. The price of the good is the control parameter. Attainable sets of the system are investigated. It is proved that only bang-bang controls with at most one switching can lead trajectories to the boundary of an attainable set. Thus, this boundary is formed by the union of two one-parameter curves; the parameter is the moment of switching. Attainable sets for different parameters of the model are constructed with the use of a computer program written in MAPLE. Possible economic applications are discussed.
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