During a preliminary survey for a $2\text{-kilometer}$ highway segment, the average end areas for cut at two consecutive stations (Station $10+000$ and Station $10+050$) are $15 \text{ m}^2$ and $25 \text{ m}^2$, respectively. If the unit cost of excavation is $\text{PHP } 350/\text{m}^3$, estimate the cost of earthwork for this $50\text{-meter}$ section.

A new residential subdivision is being planned. A transportation engineer uses a trip generation model based on household size and vehicle ownership. The developed linear regression model is $T = 1.2 + 2.5H + 1.8V$, where $T$ is the number of daily trips per household, $H$ is the number of persons in the household, and $V$ is the number of vehicles owned. If the subdivision will have $500$ households, with an average of $4$ persons and $2$ vehicles per household, calculate the total expected daily trips generated by the subdivision.

A proposed highway bypass will cost $\text{PHP } 500 \text{ Million}$ to construct with an annual maintenance cost of $\text{PHP } 5 \text{ Million}$. The existing route has an annual maintenance cost of $\text{PHP } 12 \text{ Million}$. The bypass will save motorists $\text{PHP } 30 \text{ Million}$ annually in vehicle operating costs and $\text{PHP } 25 \text{ Million}$ annually in travel time savings. Assuming a project life of $20$ years and an interest rate of $8\%$, determine if the project is economically viable using the Benefit-Cost Ratio (BCR).

A new highway is planned to connect City A and City B, separated by $120\text{ km}$ of varied terrain. Engineers have proposed three alternative routes:

Analyze the trade-offs of these routes based on the modern route selection process.

During the 19th century, two competing methods dominated road construction: Telford's method and Macadam's method. Suppose a road is being built across a region known for heavy rainfall and relatively weak subgrade soil. Analyze how each historical method would approach this challenge and which methodology is more heavily reflected in modern flexible pavement design.