Question Number 200716 by hardmath last updated on 22/Nov/23
$$\mathrm{1}.\: \\ $$$$\frac{{a}}{\mathrm{8}}\:+\:\frac{{b}}{\mathrm{5}}\:=\:\mathrm{6}\:\:\:\Rightarrow\:\:\:\left({a}+{b}\right)_{\boldsymbol{{max}}} \:=\:? \\ $$
Answered by AST last updated on 22/Nov/23
$$\mathrm{5}{a}+\mathrm{8}{b}=\mathrm{240}\Rightarrow{a}=\frac{\mathrm{240}−\mathrm{8}{b}}{\mathrm{5}} \\ $$$${remains}\:{to}\:{find}\:\left({a}+{b}\right)_{{max}} =\left(\frac{\mathrm{240}−\mathrm{3}{b}}{\mathrm{5}}\right)_{{max}} \\ $$$${If}\:{b}\geqslant\mathrm{0},\:{then}\:{max}\left({a}+{b}\right)=\frac{\mathrm{240}}{\mathrm{5}}=\mathrm{48} \\ $$$${But}\:{if}\:{b}\:{can}\:{be}\:{less}\:{than}\:\mathrm{0},{then}\:{a}+{b}\:{has}\:{no}\:{upper} \\ $$$${bound} \\ $$