Resource Allocation Problem

I worked the attached Resource Allocation Problem, but I am not sure I worked it correctly. I used intuition more than mathematical constructs. Will you take a look and let me know know the right way to do the problem?

Probabilstic Dynamic Programming

The attachted file has an example problem my professor gave. I am not sure that I have it set up right.

I need an explanation of the solution to an optimal policy problem

My professor gave us the solution to one of our homework problems, and I don't understand. The attached file contains his solution, and my questions in red. Can you please help me to understand?

I have a dynamic programming that I don't think I have set up correctly

The attached file contains a dynamic problem. I don't think I have it set up right because I keep going in circles when I attempt to solve it. Could you please help me? I am not sure where I am making my mistake.

Policy iteration problem

The attached file has a homework problem my professor assigned. I work it (also included). I don't think I have worked it correctly. Can you point me in the right direction?