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\newcommand{\resource}{{R}}
\newcommand{\plant}{{P}}
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\begin{document}

$\begin{array}{ll}
 \mbox{Maximize}\ & Z=c_1x_1+\dots+c_nx_n\\
\mbox{subject to}& \\
 & a_{11}x_1+\dots+a_{1n}x_n\le b_1\\
 & \qquad\qquad \vdots\\
 & a_{m1}x_1+\dots+a_{mn}x_n\le b_m\\
 & x_i\ge 0, 1\le i\le n.\end{array}$


$\begin{array}{ll}
 \mbox{Maximize}\ & Z=x_1+3x_2\\
\mbox{subject to}& \\
 & \quad\quad \ \ x_2\le 3\\
 & x_1+x_2\le 4\\
 & x_1+5x_2\ge 5\\
 & x_1\ge 0,\ x_2\ge 0.\end{array}$


\begin{equation}\label{eq1}
\left\{\begin{array}{l} \displaystyle{\frac{d\resource}{dt}
=r - w.\ast \resource - ({\rm diag}(\resource)\ast U^{(1)})\ast \plant}_{\ _{\ _{\ _{\ _{\ _{\ _{ }}}}}}}\\%:=\resource F(\resource,\plant,\herbivore)\\
 % \\
\displaystyle{\frac{d\plant}{dt} =  \plant.\ast ((\min({\rm
diag}(\resource)\ast (b^{(1)}.\ast U^{(1)}),[\,],1))'
- d^{(1)} - m^{(1)}.\ast \plant - c^{(1)}\ast \plant - U^{(2)}\ast \herbivore)}_{\ _{\ _{\ _{\ _{\ _{\ _{ }}}}}}}\\%:=\plant G(\resource,\plant) \\
\displaystyle{\frac{d\herbivore}{dt} =\herbivore.\ast ((b^{(2)}.\ast
U^{(2)})'\ast \plant - d^{(2)} - m^{(2)}.\ast \herbivore -
c^{(2)}\ast \herbivore - U^{(3)}\ast \carnivore)}_{\ _{\ _{\ _{\ _{\
_{\ _{ }}}}}}}
\\%:=\herbivore H(\resource,\herbivore) \\
\displaystyle{\frac{d\carnivore}{dt} =\carnivore.\ast ((b^{(3)}.\ast
U^{(3)})'\ast \herbivore - d^{(3)} - m^{(3)}.\ast \carnivore -
c^{(3)}\ast \carnivore)}
\end{array}\right.
\end{equation}

\end{document}
