A library must build shelving to shelve 200 4-inch highbooks, 100 8-inch high books, and 80 12-inch high books. 8.3 Maximum-Flow Problems 419Each book is 0.5 inch thick. The library has several ways tostore the books. For example, an 8-inch high shelf may bebuilt to store all books of height less than or equal to 8inches, and a 12-inch high shelf may be built for the 12-inchbooks. Alternatively, a 12-inch high shelf might be built tostore all books. The library believes it costs $2,300 to builda shelf and that a cost of $5 per square inch is incurred forbook storage. (Assume that the area required to store a bookis given by height of storage area times book’s thickness.)Formulate and solve a shortest-path problem that couldbe used to help the library determine how to shelve thebooks at minimum cost. (Hint: Have nodes 0, 4, 8, and 12,with cij being the total cost of shelving all books of height i and j on a single shelf.)
A library must build shelving to shelve 200 4-inch highbooks, 100 8-inch high books, and 80 12-inch high books. 8.3 Maximum-Flow Problems 419Each book is 0.5 inch thick. The library has several ways tostore the books. For example, an 8-inch high shelf may bebuilt to store all books of height less than or equal to 8inches, and a 12-inch high shelf may be built for the 12-inchbooks. Alternatively, a 12-inch high shelf might be built tostore all books. The library believes it costs $2,300 to builda shelf and that a cost of $5 per square inch is incurred forbook storage. (Assume that the area required to store a bookis given by height of storage area times book’s thickness.)Formulate and solve a shortest-path problem that couldbe used to help the library determine how to shelve thebooks at minimum cost. (Hint: Have nodes 0, 4, 8, and 12,with cij being the total cost of shelving all books of height i and j on a single shelf.)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 50P
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A library must build shelving to shelve 200 4-inch high
books, 100 8-inch high books, and 80 12-inch high books.
books, 100 8-inch high books, and 80 12-inch high books.
8.3 Maximum-Flow Problems 419
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, and 12,
with cij being the total cost of shelving all books of height
i and j on a single shelf.)
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, 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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