Question Number 10464 by ABD last updated on 10/Feb/17
Answered by mrW1 last updated on 10/Feb/17
$${for}\:\mid{x}−\mathrm{2}\mid=\mathrm{0}\:\Rightarrow{x}=\mathrm{2},\:\mid\mathrm{3}{x}−\mathrm{8}\mid=\mathrm{2} \\ $$$${for}\:\mid\mathrm{3}{x}−\mathrm{8}\mid=\mathrm{0}\:\Rightarrow{x}=\frac{\mathrm{8}}{\mathrm{3}},\:\mid{x}−\mathrm{2}\mid=\frac{\mathrm{2}}{\mathrm{3}}<\mathrm{2} \\ $$$${A}_{{max}} =\frac{\mathrm{24}}{\frac{\mathrm{2}}{\mathrm{3}}+\mathrm{0}}=\mathrm{36} \\ $$