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 the 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 the books. The library believes it costs $2300 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 books thickness.)

Formulate and solve a shortest path problem that could be used to help the library determine how to shelve the books at a minimum cost. (Hint: Have nodes 0, 4, 8 and 12 with ci,j being the total cost of shelving all books of height > i and j on a single shelf.)

Calculate c4,8 in ($).