To integer programming, algebraic approaches using GrObner bases and standard pairs via teric ideals have been studied in recent years. In this papcr, we consider a unimodular case, e.g., network flow proble[ns, which enables us to anal}rze primal and dual problem$ in an equal settlng. By cembining existing results in an algebTaic approach, we provc a theorcm that tlie maocimum nuniber of dual feaslble bases is obtained by computing the normalized volumc of the convex hull generated from column

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... vectors of a coeencient matrix in the primal standard l'orin. We apply the theorem, partly with Gr6bner bases theory, to transportat,ion problems and minimum cost flow problerns on acyclic tournament graphs. In consequence, we show new algebraic pToofs to the Balinski and Russakoff's rcsult on the dual transportation polytope and Klee aiid Witzgall's result on the priinal tr'ansportation polytopc, Siinilarly results for tlLe prinial case of acyclic tournament graphs are obt,ained b"' using Gel± 'and, Graev and Postnikov's result for iiilpotent hypergeometric functions. INe also give a boulld of the number of feasible bases for its dual case.