Based on Ravindran (1971). A library must buildshelving to shelve 200 4-inch-high books, 600 8-inchhighbooks, and 500 12-inch-high books. Each bookis 0.5 inch thick. The library has several ways to storethe books. For example, an 8-inch-high shelf can bebuilt to store all books of height less than or equal to8 inches, and a 12-inch-high shelf can be built for the12-inch books. Alternatively, a 12-inch-high shelf canbe built to store all books. The library believes it costs$2300 to build a shelf and that a cost of $5 per squareinch is incurred for book storage. (Assume that thearea required to store a book is given by the height ofthe storage area multiplied by the book’s thickness.)Determine how to shelve the books at minimumcost. (Hint: We agree that this is not a very realisticproblem in terms of how a library operates, but it isa good modeling challenge. Create nodes 0, 4, 8, and12, and make the cost associated with the arc joiningnodes i and j equal to the total cost of shelving allbooks of height greater than i and less than or equal toj on a single shelf.)
Based on Ravindran (1971). A library must build
shelving to shelve 200 4-inch-high books, 600 8-inchhigh
books, and 500 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 can be
built to store all books of height less than or equal to
8 inches, and a 12-inch-high shelf can be built for the
12-inch books. Alternatively, a 12-inch-high shelf can
be built to store all 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 the height of
the storage area multiplied by the book’s thickness.)
Determine how to shelve the books at minimum
cost. (Hint: We agree that this is not a very realistic
problem in terms of how a library operates, but it is
a good modeling challenge. Create nodes 0, 4, 8, and
12, and make the cost associated with the arc joining
nodes i and j equal to the total cost of shelving all
books of height greater than i and less than or equal to
j on a single shelf.)
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