- This proof says if $Z_P \ne Z_Q$...
...then $Z$ is maximised (or minimised, I guess) at one of the $\color{red}{\text{endpoints}}$ -- of what exactly? $\overline{PQ}$? So the maximum value of $Z$ occurs at either $P$ or $Q$?
Is the last statement in the $\color{red}{\text{red}}$ boxes below supposed to say 'will be maximised' rather than 'will increase'?
Is the statement (either original or revised to 'increased') justified by the statement indicated by the $\color{blue}{\text{blue}}$ boxes? There's no statement like 'by our result above' sooooo.......
Both screenshots from Chapter 2 here.