Based on traffic data collected from an expressway, a Highway Engineer established that the space-mean speed ,(km/h) and density k (vehicles/km) relationship follows closely to the Greenberg model: v, = c In(k;/k), where k; is the jam density. (a) Assuming traffic is homogeneous, establish the flow-density relationship (b) By differentiation, find the density and speed at maximum flow in terms of k; and c (c) Given that c = 30km/h and k; = 150 veh/km, plot the graphs for each of the three relationships using Microsoft Excel i. Speed - Density ii. Speed - Flow iii. (d) Verify based on results in (c) that the maximum flow is the product of speed and the density at which it is attained Flow Density