1. Graph coloring application. Eight cheenicals are to be Wrte legilbly The cost of doing this depends on the suanber of tnoxes s 73. Each additional box rusts S100to mininike chemicals interact with ooe another and it is too risky ta shipped acrouss coantry by air express ). We wish to minimize the bumber of bosss. However, soe o ship them is the same container. The Ntusingel ng .., es and chemicals that nteraet with given chmien1 follows: (a) Model this infomation with a graph: & repesents t he veries CB) Cz Ca ) Determine a minimam coloring of the graph using the integers (1, 2, ...) rather than colors. Write these "colors legibly next to the vertices. What is the chromatic number of this graph? ) How should the chemicals be packed into boxces so no two which interact will be in the same one? Le., determine what chemicals are in which boo. t of shipping the chemicals