Rear$-$dump trucks with below specifications are used to haul sandy clay material. The performance chart of the trucks is shown as below. The trucks have below information:

Capacity: heaped, $19$cy

Net weight empty: $36,860$ lbs

Payload: $44,000$ lbs

Gross vehicle weight: $80,860$ lbs

The trucks will be loaded by a hydraulic hoe with $3\mathrm{.}25$ cy bucket. The haul route from loading to the waste site is $3\mathrm{.}5$ mile downhill grade of $1\%.$ The haul route will be on

earth, poorly maintained with a rolling resistance of $120l\frac{b}{t}on.$ Dump time will be average $2$ min and the hoe loading cycle is $25$ sec $.$ The sandy clay has a loose unit weight of $2,500l\frac{b}{c}y.$ An efficiency factor is applied for a $50-$min hour. The bucket fill factor of the sandy clay is $110\%,$ and $100\%$ for the truck. How many trucks are ideal for this operation? $(30$ points$)$