  In this paper, we present a simple microeconomic model with linear
continuous-time dynamics that describes a production-inventory system with debt
repayment. This model is formulated in terms of optimal control and its exact
solutions are derived by prudent application of the maximum principle under
different sets of initial conditions (scenarios). For a potentially profitable
small firm, we also propose some alternative short-term control strategies
resulting in a positive final profit and prove their optimality. Practical
implementation of such strategies is also discussed.
