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fix formattazione di alcuni esercizi di teoria

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stefanogoldoni 2022-01-08 19:33:12 +01:00
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@ -24,7 +24,7 @@
\title{Gran Compendio OLI} \title{Gran Compendio OLI}
\author{\href{https://github.com/meschio94/Gran-Compendio-OLI}{Meschio}} \author{\href{https://github.com/meschio94/Gran-Compendio-OLI}{Meschio}}
\date{2021\\V1.2.1} \date{2021\\V1.2.2}
\begin{document} \begin{document}
\maketitle \maketitle
@ -1428,8 +1428,7 @@ Soluzione:\\
\subsection{PLC minimization} \subsection{PLC minimization}
\noindent\fbox{% \noindent\fbox{%
\parbox{\textwidth}{% \parbox{\textwidth}{%
Given a PLC problem P in minimization form, with 2 constraints with sign ’≥’ and 1 Given a PLC problem P in minimization form, with 2 constraints with sign '$\geqq$' and 1 constraint with sign '=', and 5 variables, consider the dual problem D:
constraint with sign ’=’, and 5 variables, consider the dual problem D:
\begin{enumerate}[label=\Alph*] \begin{enumerate}[label=\Alph*]
\item | D has 3 variables \item | D has 3 variables
and 5 constraints; and 5 constraints;
@ -1519,7 +1518,8 @@ The branch-and-cut method:
\begin{enumerate}[label=\Alph*] \begin{enumerate}[label=\Alph*]
\item | is used to solve linear programming problems with continuous variables; \item | is used to solve linear programming problems with continuous variables;
\item | always uses the lowest-first strategy to explore the subproblems.; \item | always uses the lowest-first strategy to explore the subproblems.;
\item | is used to solve NP-complete (“difficult”) problems; (d) terminates in a polynomial number of iterations; \item | is used to solve NP-complete (“difficult”) problems;
\item | terminates in a polynomial number of iterations;
\item | at each iteration uses the simplex algorithm to solve the current subproblem. \item | at each iteration uses the simplex algorithm to solve the current subproblem.
\end{enumerate} \end{enumerate}
}% }%
@ -1532,8 +1532,11 @@ Soluzione:\\
\parbox{\textwidth}{% \parbox{\textwidth}{%
Given a PLC problem with $n$ variables and $m$ constraints, a basic matrix is: Given a PLC problem with $n$ variables and $m$ constraints, a basic matrix is:
\begin{enumerate}[label=\Alph*] \begin{enumerate}[label=\Alph*]
\item | a collection of $m$ constraints; (b) none of the above answers.; \item | a collection of $m$ constraints;
\item | a square $m$x$m$ matrix with value 1 on the main diagonal; \item | a collection of $n-m$ columns of the constraint matrix; \item | a square submatrix of the constraint matrix, that can be inverted. \item | none of the above answers.;
\item | a square $m$x$m$ matrix with value 1 on the main diagonal;
\item | a collection of $n-m$ columns of the constraint matrix;
\item | a square submatrix of the constraint matrix, that can be inverted.
\end{enumerate} \end{enumerate}
}% }%
}% }%