Competition between populations: In this exercise we consider the problem of competition between two populations that vie for resources but do not prey on each other. Let m be the size of the first...

Competition between populations: In this exercise we consider the problem of competition between two populations that vie for resources but do not prey on each other. Let m be the size of the first population, let n be the size of the second (both measured in thousands of animals), and assume that the populations coexist eventually. An example of one common model for the interaction is

At an equilibrium point the per capita growth rates for m and for n are both zero. If the populations reach such a point, then they will continue at that size indefinitely. Find the equilibrium point in the example above.