You have n items with weights x$1,$x$2,.....$xn$,$ where $0$x$\_$i$1$ for all i$,$ arriving one item at a

time. You want to pack them in the minimal number of bins, where each bin can hold a maximum

weight of $1.$ As each item comes in$,$ you must immediately assign it to a bin without knowing the

weights of future items. Consider the strategy that assigns the arriving item to the last bin that has

been opened if it fits, and open a new bin otherwise. Show that this strategy achieves a competitive

ratio of $2.$