\(C\ge2021\)
Dấu bằng xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}2x-3=0\\3y+1=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=-\dfrac{1}{3}\end{matrix}\right.\)
Vậy \(C_{Min}=2021\) khi \(x=\dfrac{3}{2}\) và \(y=-\dfrac{1}{3}\)
Vì |2x - 3| \(\ge\) 0, \(\forall\)x ; |3y + 1| \(\ge\) 0,\(\forall\)y
\(\Rightarrow\) C = 2020|2x - 3| + 2021|3y + 1| + 2021 \(\ge\) 2021, \(\forall\)x,y
Dấu " = " xảy ra khi và chỉ khi :
\(\left\{{}\begin{matrix}\left|2x-3\right|=0\\\left|3y+1\right|=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=-\dfrac{1}{3}\end{matrix}\right.\)
Vậy Cmin = 2021 với \(x=\dfrac{3}{2};y=-\dfrac{1}{3}\)
