The paper presents formulations of three optimizing problems designed to minimize the servicing cost of central government debt - the key component of overall public debt. The first two problems allow to minimize the servicing costs (both discount and coupon) of debt instruments sold at the same auction - whether Treasury bills or fixed-rate bonds. The third one determines the optimal structure of new debt, both domestic and foreign, within a longer time horizon, e.g. a few years. The first two problems are of a deterministic nature, i.e. they do not include the random factor. The third one is based on the Markovitz model (originally developed to optimize an investment portfolio) in which future yields are assumed to be multivariate random variables with a known vector of expected values and known variance and covariance matrix. The problems presented in the paper can be applied to support decisions made by the issuer of debt. The paper also includes basic information on the sale of debt instruments. Finally, directions in the modification of the formulated problems are indicated.