Joe wants to sell his car. Every month he receives an offer and must decide whether to accept

or reject the offer immediately. Once rejected, the offer disappears. The possible offers are

$$600,$$$800$ and $$1,000$ with probabilities $\frac{5}{8},\frac{1}{4}$ and $\frac{1}{8}$ respectively $($consecutive offers are

independent of each other$).$ The monthly maintenance cost for the car is $$60.$ Since Joe wants

to sell the car, he chooses the discount factor $=0\mathrm{.}95.$ Find a policy that minimizes the total

expected discounted cost. $($Hint: There are two actions: Accept or reject the offer. For month

$t,$ set the state to be the offer made that month. Also include a state with a monthly cost of $0,$

which becomes the state when the offer is accepted$).$