Menu Close

1-a-8-b-5-6-a-b-max-




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

Leave a Reply

Your email address will not be published. Required fields are marked *