A library must build shelving to shelve $2004-$inch high books, $1508-$inch high

books, $30010-$inch high books and $18012-$inch high books. Each book is $0\mathrm{.}5$ 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 $$2,000$ to build a shelf and that a cost of $$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.$)$