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Problem 3: A library must build shelving to shelve 200 4-inch high books, 100 8-inch high books and 80 12-inch high books. Each book is 0.5 inch thick. The library has several ways to store the books. For example, an 8-inch high shelf may be built to store all books of height less than or equal to 8 inches, and a 12-inch high shelf might be built for the 12-inch books. Alternatively, a 12-inch high shelf might be built to store all books. It costs $2,300 to build a shelf plus $5 per square inch of book storage. (Assume the area required to store a book is given by the height of storage area times the book's thickness.) Formulate a shortest path problem that could be used to help the library determine how to shelve the books at minimum cost. For this problem, you should provide a drawing of the network. Explain in words what nodes and arcs represent, and label nodes and arcs with all relevant data. (Hint: Have nodes 0, 4, 8, and 12 with an arc (i,j) representing the decision to store all books of height > i and sj on a single shelf.)