Problem 1 Consider the shortest path models for the knapsack and inspection scheduling problems discussed in the lecture. Note that the shortest path model for the lmapsack problem has a treelike structure {it is not a treellj with the property that any node in the directed network describes precisely how much weight capacity has been consumed in your consideration of objects so far. The directed graph of the model was constructed is such a way that your options about the next object, whether you can say \"yes or \"no? show up as distinct out-going arcs. and the arcs you choose in this way encodes your sequence of yeslfno decisions objects. Note also that this property is not true of the shortest path model we developed for the inspection scheduling problem, where the graph describes solutions to the scheduling problem in terms of the intervals between successive inspections. The purpose of this problem is to explore alternative shortest path models for each of these problems. 1. Develop a shortest path model for the inspection scheduling problem where the directed network of the model encodes sequences of yesfno decisions about whether to inspect each stage. Express your answer graphically as a directed network showing all of the nodes and arcs necessary for a problem involving four stages of production. [Do not attach numerical values indicating arc costs; we only need to see the \"topology of your graph.) 2. Consider a knapsack problem involving four objects, each of which can be selected at most once. Is it possible to use a network topology like that developed for the \"Inspection Scheduling Problem\"? Does that topology work? Do you know how to attach costs to the arcs so that the shortest st path actually corresponds to the optimal solution to the knapsack