Question

\(\left\{{}\begin{matrix}2x+y< =4\\x+2y< =4\\x>=0\\y>=0\end{matrix}\right.\)

tìm max của hệ

Answer 1

\(Hpt\Leftrightarrow\left\{{}\begin{matrix}4x+2y\le8\\x+2y\le4\\x\ge0\\y\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}0\le x\le\dfrac{4}{3}\\0\le y\le\dfrac{4-x}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}0\le x\le\dfrac{4}{3}\\0\le y\le\dfrac{4-\dfrac{4}{3}}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}0\le x\le\dfrac{4}{3}\\0\le y\le\dfrac{4}{3}\end{matrix}\right.\)

Vậy \(\left(x;y\right)_{max}=\left(\dfrac{4}{3};\dfrac{4}{3}\right)\)