Question

Calculate the minimum cost of this operation given that:

The transportation costs are $5.00 per cubic yard per mile

The cost of dumping excess material in the spoil area is $0.50 per cubic yard

The cost to excavate for the borrow pit is $1.00 per cubic yard

No more than 50,000 cubic yards can be cut from the borrow pit

Spoils area Fill 15,000 yd3 2 mi Cut 20,000 yd3 Cut 10,000 yd3 Fill 20,000 yd3 Cut 30,000 yd3 10 mi 2 mi-10 mi 5 mi- Not to scale Borroww pit Fill 15,000 yd3

Example 1 (Contd): .The figure in the previous slide shows a cut and fill operation in a highway construction site. . There are 3 cut and 3 fill areas as well as a borrow pit and a spoil area. .The amount of dirt needed to be cut in each cut area and filled in each fill area is given in the figure. If needed, we can cut material from borrow pit and dump excess material in the spoil areaa We would like to complete this operation at minimum cost given that: The transportation costs are $5.00 per cubic yard per mile The cost for dumping excess material in the spoil area is $0.50 per cubic yard The cost to excavate from the borrow pit is $1.00 per cubic yard No more than 50,000 cubic yards can be cut from the borrow pit

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