Alibrary 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 book’s thickness.)