\(\left\{{}\begin{matrix}P+N+E=13\\P=E\\P\le N\le1,5P\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}2P+N=13\\P\le N\le1,5P\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}N=13-2P\\P\le13-2P\le1,5P\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}N=13-2P\\3P\le N\le3,5P\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}N=13-2P\\4,333>P\ge3,714\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}P=E=4\\N=13-2.4=5\end{matrix}\right.\)