At the beginning of each year, an aircraft engine is in good, fair, or poor condition. It costs $500,000 to run a good engine for a year, $1 million to run a fair engine for a year, and $2 million to run a poor engine for a year. A fair engine can be overhauled for $2 million, and it immediately becomes a good engine. A poor engine can be replaced for $3 million, and it immediately becomes a good engine. The transition probability matrix for an engine is as follows:

a) Determine the policies that could arise and solve 1 of them.

b) Determine the optimal maintenance policy over the next few years (infinite horizon) by linear programming only.

GoodGoodPoorFair.70Fair.2.60.1.41Poor GoodGoodPoorFair.70Fair.2.60.1.41Poor