An excavation company has been contracted to supply 10 million cubic feet (cu. ft.) of dirt to a construction site. The company uses a bulldozer to collect dirt, which is then moved by a dump truck to the construction site. It costs the company $100 per hour to use the bulldozer, and it rents dump trucks at a rate of $40 per hour per truck. Each dump truck can hold 1,000 cu. ft. of dirt, and it takes an average of 12 minutes for the bulldozer to load a dump truck with dirt. It takes an average of five minutes for a fully loaded dump truck to deliver the dirt to the construction site and returns to the bulldozer for another load.

Assume that the time to load a dump truck and the time for a dump truck to deliver the dirt to the construction site and return to the bulldozer follow exponential distributions. Moreover, a usual trip of the truck involves load with dirt, deliver the dirt, return to the bulldozer where it joins a queue for another load of dirt.

Then, determine the most appropriate queuing model for the dirt-moving process and then use that model to determine how many dump trucks to rent in order to minimize the expected cost of fulfilling the contract.