For the herd model described in Example 2, let the parameters be given by b = 0.9, d_{1}=0.1, \text { and } d_{2}=0.2 . \text { Thus } x _{k}=A x _{k-1}, where
A=\left[\begin{array}{cc}0 & .9 \\.9 & .8-h\end{array}\right].
Determine a harvest rate h so that the herd neither dies out nor grows without bound.