Abstract. We prove that the maximum singular value of the matrix and the corresponding singular vectors are the optimal solution for a special quadratic extremal problem. We consider the economic interpretation of the optimal solution for the linear model of production and for the productive Leontief model. We relate the optimal solution to the Frobenius number and vectors and compare the Frobenius numbers and maximum singular values for Leontief inverse matrix in the 15-sectoral balance of Ukraine for 2003–2009.

Keywords: maximum singular number, quadratic optimization problem, Frobenius number and vectors, irreducible matrix, Leontief inverse matrix.