Chapter 5 Discrete Markov process Suppose we have a sequence of random variables, {X0 , X1 , .} = {Xn } , which is also n=0 called a stochastic...

Okay, so I am not getting the help I desire to understand how this problem should be solved.  This is a Stochastic Operational Research class using calculus and probability to build Markov Chains or Transitional and Steady State Probability Matrixes to solve.  In this case, I just do not know how to start.  The help I have gotten so far has not been even close to right.  Is there anyone who has a clue out there that can help me set this up and solve it?  I have attached the chapter to this post so you can see what I am dealing with.  I really need help from someone who understands how this works.

 During any month, Cashco has a .5 chance of receiving a $1,000 cash inflow and a .5 chance that there will be a $1,000 cash outflow. For every $1,000 in cash on hand at the end of a month, Cashco incurs a $15 cost (due to lost interest). At the beginning of each month, Cashco can adjust its on-hand cash balance upward or downward with the cost per transaction being $20. Cashco can never let the on-hand balance become negative. The company is considering the following two cash management policies:

Policy 1 At the beginning of a month in which the on hand cash balance is $3,000, immediately reduce the cash balance to $1,000. At the beginning of a month in which the on-hand cash balance is $0, immediately bring the on-hand cash balance up to $1,000.

Policy 2 At the beginning of a month in which the on hand cash balance is $4,000, immediately reduce the cash balance to $2,000. At the beginning of a month in which the on-hand cash balance is $0, immediately bring the on-hand cash balance up to $2,000. 

Which policy will incur a smaller expected monthly cost (opportunity plus transaction)? The sequence of events during each month is as follows:

a) Observe beginning cash balance

b) Adjust (if desired) cash balance

c) Cash balance changes

d) Opportunity cost is assessed