Problem 2: A certain country is divided into two regions called "West" and "East".  In the absence of any migration
into or out of the region, the West population would decline by 1% per year while the East population would remain constant (zero population growth).  However, 2% of West inhabitants per year move East and 1% of East inhabitants move West.

a. Write a system of two linear differential equations for the rates of change of West and East population numbers, if there is no immigration from the outside.
 

b.  What is the long term rate of decline of these population numbers, if there is no outside immigration?
 

c.  If there is outside immigration into West and East, each at a rate of one-half million per year, what are the equilibrium population numbers in each region.