2. 10 marks] Recall the online bin packing problem: Given numbers s1., Sn one-by-one, where 0S si 1, pack them into a minimum number of unit-capacity bins. The decision of what bin to put item si in must be made without knowledge of items si+1,., Sn- In class we saw an algorithm, First Fit, that packs the items into at most 20PT+1 bins, where OPT is the minimum number of bins required for the items (assuming perfect information about all the items). In this problem, we will suppose that the bins are also "online" in the sense that we pack items into the current bin until some item does not fit, then we close that bin and start a new bin. More precisely, the algorithm is: for i 1...n if si fits in bin j, put it in else jj+1 and put si in bin j Prove that this algorithm uses at most 20PT+1 bins, i.e., it is an asymptotic 2-approximation. Notation: let m be the number of bins used by the algorithm. Let by, 1 j 1