Your Company has a contract to excavate 1 km of pipeline. The trench is 1.5 m wide and 2 m deep. They use an excavator to excavate. The excavator has a 1.5 m3 bucket. The soil has a swell factor of 25%. The trucks available to carry the excavated soil are of 12 m3 capacity. The estimated excavator cycle (excavate, swing, load, swing) is 1.5 minutes. The dumping area for the excavated soil is about 12 km away. An empty truck can travel at a speed of 50 km/h. When fully loaded, its speed is reduced to 35 km/h. Allow 3 minutes for waiting at traffic lights and 1.5 minutes for dumping the soil. Due to extreme hot weather, 50 minutes of work would require 1 hour to complete for the trucks. The daily cost of operating the excavator and truck are $700 and $400, respectively. The daily overhead charges for excavation manpower comprising, supervisor, banksman and others are $300.

(a)Determine the optimal number of trucks (for minimum costs), the total costs and duration for the excavation operation. Assume 8 hours working time per day.

(b)If the trench must be supported, and each crew can strut 5 m of trench per hour, how many trenching crews will you require to maintain the production rate of your earlier decision?