The railway between the towns of A and B spans 800 km through mountainous terrain. The total one-way travel time, t_r, is 20 hrs and currently the fare, c_r, is 600/ton. As the service is used at low capacity t_r is a constant, independent of the traffic volume V_r.

There is a lorry service competing with the railway in an approximately parallel route; its average speed is 50 km/hr and it charges a fare of 950/ton. There is a project to build a highway in order to replace the present road; it is expected that most of its traffic will continue to be heavy trucks.

The level-of-service function of the new highway has been estimated as:

t_t = 7 + 0.08V_t (hours)

where V_t is the total flow of trucks per hour.

On the other hand the railway has estimated its demand function as follows:

(V_r/V_t) = 0.83(t_r/t_t)^0.8(c_r/c_t)^1.6

and it is expected that the total volume transported between the two towns, V_r + V_t, will remain constant and equal to 200 truckloads/hr in the medium term.

(a) Estimate the current modal split (i.e. volumes transported by rail and lorry).

(b) Estimate modal split if the highway is built.

(c) What would be the modal split if:

1.The railway decreases its fare to 450/ton?

2.The lorries were charged a toll of 4/ton in order to finance the highway?

3.Both changes are simultaneous?