A transit line is to be constructed so that people living in a 200-km-long, narrow corridor can be transported to a single employment location at the end of this corridor. The transit vehicles will transport commuters to the employment location at an average travel speed of 40 km/hr for a (flat) fare of $5 per trip. People value their time at $20/hr.
Part a
Adults living in this corridor would derive a daily economic benefit of $50 by commuting (one-way) on this system. Determine a suitable length, L, for this transit line, recognizing that there is no need to extend the line beyond a distance that people are willing to travel.
Part b can be solved without solving part a]
A small community of 200 adults living outside the transit corridor would derive daily economic benefits from using the transit system. We assume these benefits are logistically distributed with average a. These 200 adults also value their time at $20/hr and they face an added cost of spending 0.25 hrs traveling by shuttle bus from their community to a (single) designated station. The station resides on our transit line at a distance x (km) from the destination (the employment location). The fare for the shuttle bus is F ($) each trip.
Write an expression for the predicted number of adults from this community that will use our transit system.