ibrary must build shelving to shelve 200 4-inch high books, 150 8-inch high books, 300 10-inch high books and 180 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 may be built for the 12-inch books. Alternatively, a 12-inch high shelf might be built to store all books. The library believes it costs $2,300 to build a shelf and that a cost of $5 per square inch is incurred for book storage. (Assume that the area required to store a book is given by height of storage area times book’s thickness.) Formulate and solve a shortest-path problem that could be used to help the library determine how to shelve the books at minimum cost. (Hint: Ha
A library must build shelving to shelve 200 4-inch high books, 150 8-inch high books, 300 10-inch high books and 180 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 may be built for the 12-inch books. Alternatively, a 12-inch high shelf might be built to store all books. The library believes it costs $2,300 to build a shelf and that a cost of $5 per square inch is incurred for book storage. (Assume that the area required to store a book is given by height of storage area times book’s thickness.) Formulate and solve a shortest-path problem that could be used to help the library determine how to shelve the books at minimum cost. (Hint: Have nodes 0, 4, 8, 10 and 12, with cij being the total cost of shelving all books of height >i and ≤ j on a single shelf.)
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