Problem $2(10$ pts$).$ The capacity of a highway is suddenly reduced to $60\%$ of its normal

capacity due to closure of certain lanes in a work zone.

If the Greenshield model defines the relationship between speed and density for this

highway, $($the highway jam density is $112ve\frac{h}{h}r,$ and the mean free speed is $64\mathrm{.}5mph,)$

calculate the capacity of the highway. $(2$ pts$)$

Calculate the regular capacity of the highway. $(1$ pt$)$

Determine arrival flow if it is at $80\%$ of regular capacity. $(1$ pt$)$

What are the values of space mean speed and density in steady $($uncongested$)$ flow,

upstream of the work zone region? $(2$ pts$)$

What are the values of space mean speed and density in the congested vicinity of the

work zone $(2$ pts$)?$

What are the reduction and increase in space mean speed and density by the work zone?

$(2$ pts$)$