Consider the greedy algorithm for the bin$-$packing problem, which is called the first$-$fit $($FF$)$ algorithm: place each of the items in the order given into the first bin the item fits in; when there are no such bins, place the item in a new bin and add this bin to the end of the bin list. a$.$ Apply FF to the instance s$1=0\mathrm{.}4,$ s$2=0\mathrm{.}7,$ s$3=0\mathrm{.}2,$ s$4=0\mathrm{.}1,$ s$5=0\mathrm{.}5$ and determine whether the solution obtained is optimal. b$.$ Determine the worst$-$case time efficiency of FF$.$ c$.$ Prove that FF is a $2-$approximation algorithm.