At the beginning of each year, an aircraft engine is in good, fair or poor condition. It costs $500,000 to operate a good engine for one year, $1 million to operate an engine in fair condition for one year and $2 million to operate an engine in poor condition for one year. An engine in fair condition can be reconditioned for $2 million and immediately becomes a new engine. An engine in poor condition can be replaced for $3 million and 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.