A contractor has a fleet of dump trucks for moving construction debris. The cost of running this fleet is $325/hr per truck. For a given contract, a total of 2,500 tons must be removed from one construction site and moved to another location 35 miles away. The average round-trip truck speed diminishes with its load by the equation: S = 40 - 1.75*L, where L is the truckload (in tons) and S is the truck speed (in mph). Time is also required for loading trucks. The time required to load a truck is given by F = 0.3*(L^0.5), where F is in hours.
(a) Develop a cost function for the total cost of removing the debris as a function of each truck's load.
(b) Using calculus, find the individual truckload, which minimizes the contractor's total cost for removing the debris. What is the total cost? (Be sure your solution is a minimum!)
(c) Does the distance the debris is moved affect this optimal loading? Does it affect the total cost? Justify your answer.
(d) How is this optimal loading changed if the maximum truck speed is changed from 35 to 45 mph or to 25 mph? What would these changes do to the cost of this particular job?