Explain how you would set up the application problems:$[$you do not need to actually solve them unless you just want to$]$

$1.$ A rectangular box is resting on the xy plane with one vertex at the origin.$$ Find the maximum volume of the box if its vertes opposite the origin lies in the plane $6$x$+4$y$+3$z $=24$

$2.$ The material for constructing the base of an open box costs $1\mathrm{.}5$ times as much as the material for constructing the sides.$$ For a fixed amount of money, C$,$ find the dimensions of the box of largest volume that can be made.