A case study of the tools used by an analyst of the economic aspects of the operation of the water supply network has been undertaken in this paper. All issues discussed here are formulated by using degenerated linear programming models ( PL ). Below, it is noted that the linear dependence of binding constraints ( CO ) distorts standard postoptimization procedures in PL. This observed fact makes postoptimization analysis mostly unhelpful for an average analyst due to problems with the int erpretation of ambiguous sensitivity reports which are obtained from popular computer packages. In standard postoptimization methods, changes to single parameters of the right-hand vector CO are analyzed or referred to parametric linear programming that unfortunately requires prior knowledge of mathematically and economically justified vectors of changes of right-hand sides CO. Therefore, it is suggested that modifications are introduced to some of the postoptimization procedures in this work. For issues in the field of hydrology, the following were presented: interpretation and methods of generating justified vectors of changes of right-hand sides of limiting conditions. And so, the procedure of generating infinitely many solutions of the dual issue based on certain vectors orthogonal to the vector of right-hand sides of constraint conditions was demonstrated. Furthermore, the same orthogonal vectors were used to obtain nodal solutions of the dua0l model and the corresponding vectors of changes of the entire right-hand sides of the constraint conditions. Then, managerial interpretation was applied to this way of proceeding. The methods presented in the work serve to improve the functioning of the system of water supply.

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A bstvxtSeveral theorems on estimation and verification of linear hypotheses in some iiiodels are given. The assumptions are as follows. Let y=Xp + e or (y, Xp, uZV) be a fixed model whei~e y is a vector of n observations, X is a known matrix n x p with rank r ( X ) = r s p < n , where 1' is H. number of coordinates of the unknown parameter vector p. e is a random vector of errom wit.11 covariance matrix a'V, where u2 is unknown scalar parameter, V is a known non-negative definite matrix such that R ( X ) c R( V). Symbol R(A) denotes a vector epace generated by columns of iiiatrix A. The expected value of y is Xp. In this paper four following Zyskind-Martin (ZM) inodels are considered: ZMd, ZMa, ZMc and ZMqd (definitions in sec. by minimization of the residual sum of squares is recommended in several papers and books. DODGE (1984) examines published methods for analyzing designed experiment with missing observations. I n this paper YATES' method is used t o estimate vector of missing values to substitute it b y an estimator and to analyse the data (estimating and verification of hypotheses) in the case of a ZYSKIND

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Article citation info: (*) Tekst artykułu w polskiej wersji językowej dostępny w elektronicznym wydaniu kwartalnika na stronie www.ein.org.pl Introduction Fixing the price of water in order to balance water demandAn analysis conducted by the World Bank [64] indicates that water shortages in some regions may reduce GDP by up to 6% and lead to increased migration and in some cases to a greater risk of conflict. Droughts and periods of water scarcity have become a more common and more frequent phenomenon in Europe [17]. The drought experiences in Europe in 2011, 2012, 2015 and 2018 were the worst in a century and affected not only Southern and Western Europe, but also the countries in Northern Europe (including Great Britain, France, Germany, Sweden and Poland). The difference between water supply and its growing demand also determines the key limitations of China's economic development. It is estimated that before 2005 due to a shortage of water in production, China lost $ 28 511 million annually. Brown [7] concluded that the shortage of water in China will soon be a threat to global cereal demand. Therefore, water, alongside cereals and crude oil, is referred to as a strategic resource. Hence, it is suggested that public authorities should shape water pricing for users in order to reflect its true shortage or alternative costs [15].