A chemical company produces two chemicals, denoted by 0 and 1,and only one can be produced at a time. Each month a decision ismade as to which chemical to produce that month. Because the demandfor each chemical is predictable, it is known that if 1 is producedthis month, there is a 70 percent chance that it will also beproduced again next month. Similarly, if 0 is produced this month,there is only a 20 percent chance that it will be produced againnext month.

To combat the emissions of pollutants, the chemical company hastwo processes, process A, which is efficient in combating thepollution from the production of 1 but not from 0, and process B,which is efficient in combating the pollution from the productionof 0 but not from 1.   Only one process can be used at atime. The amount of pollution from the production of each chemicalunder each process is

	0	1
A	100	10
B	10	30

Unfortunately, there is a time delay in setting up the pollutioncontrol processes, so that a decision as to which process to usemust be made in the month prior to the production decision.Management wants to determine a policy for when to use eachpollution control process that will minimize the expected totaldiscounted amount of all future pollution with a discount factor of0.5.

Suppose now that the company will be producing either of thesechemicals for only 4 more months, so a decision on which pollutioncontrol process to use 1 month hence only needs to be made threemore times.

a) Define Stage, states, and alternatives.

b) Formulate the cost matrix.

c) Identify the stationary policies.

d) Formulate the transition matrix.

e) Find an optimal policy for this three-period problem.