a$)$ A manufacturer wishes to produce cylindrical fruit juice cans with a capacity of $250$ ml$.$ What dimensions will minimize the amount of material required for a can? $(1$ ml $=1$ cm$3).$

$($Volume of the cylinder: r$2$h$,$  Surface area of the cylinder: $2\backslash$pi rh$+2$r$2)$

b$)$ Find the point $($x$,$ y$)$ on the graph of y$=$x nearest the point $(4,0).$