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In this paper, we present a simple microeconomic model with linearcontinuous-time dynamics that describes a production-inventory system with debtrepayment. This model is formulated in terms of optimal control and its exactsolutions are derived by prudent application of the maximum principle underdifferent sets of initial conditions (scenarios). For a potentially profitablesmall firm, we also propose some alternative short-term control strategiesresulting in a positive final profit and prove their optimality. Practicalimplementation of such strategies is also discussed.

Linear dynamic model of production-inventory with debt repayment: optimal management strategies