For the two-state, two-action problem (Example 1), write a Mathematica program to compute the sequence of functions generated by the method of successive approximations, until a termination condition is achieved, which stops the computation after the successive approximating functions differ by no more than a desired tolerance. The program should output the number of iterations necessary to terminate and the final function \(w_{n}\). Run the program for the initial function \(w_{0}(1)=w_{0}(2)=0\) and for the initial function \(w_{0}(1)=40, w_{0}(2)=30\), and find the number of iterations necessary to make the successive approximations differ by no more than .01 .