Leveling the Terrain for a New Highway, Stark and Nicholes (1972). The Arkansas Highway Department is planning a new 10-mile highway on uneven terrain as shown by the profile in Figure 2.13. The width of the construction terrain is approximately 50 yards. To simplify the situation, the terrain profile can be replaced by a step function as shown in the figure. Using heavy machinery, earth removed from high terrain is hauled to fill low areas. There are also two burrow pits, I and II, located at the ends of the 10-mile stretch from which additional earth can be hauled, if needed. Pit I has a capacity of 20,000 cubic yards and pit II a capacity of 15,000 cubic yards. The costs of removing earth from pits I and II are, respectively, $1.50 and $1.90 per cubic yard.

The transportation cost per cubic yard per mile is $.15, and the cost of using heavy machinery to load hauling trucks is $.20 per cubic yard. This means that a cubic yard from pit I hauled 1 mile will cost a total of 11.5 + .202 + 1 * .15 = $1.85 and a cubic yard hauled 1 mile from a hill to a fill area will cost .20 + 1 * .15 = $.35. Develop a minimum cost plan for leveling the 10-mile stretch.