A problem in the study of production smoothing leads to the problem of minimizing a linear form \documentclass{aastex}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{pifont}
\usepackage{stmaryrd}
\usepackage{textcomp}
\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$L(x) = \sum^{N}_{i=1}c_{i}x_{i}$
\end{document} subject to constraints of the type xi ≧ 0, \documentclass{aastex}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{pifont}
\usepackage{stmaryrd}
\usepackage{textcomp}
\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$\sum^{k}_{i=1}x_{i}\geqq r_{k}$
\end{document}. A computational solution of this problem is given, using the methods of dynamic programming.