The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows:

Let H

$=$

$$High resistance to rezoning

L

$=$

$$Low resistance to rezoning

P

$($

H

$)$

$=$

$0$

$.$

$5$

$5$

$$ P

$($

s

$1$

$|$

$$H

$)$

$=$

$0$

$.$

$1$

$8$

$$ P

$($

s

$2$

$|$

$$H

$)$

$=$

$0$

$.$

$8$

$2$

P

$($

L

$)$

$=$

$0$

$.$

$4$

$5$

$$ P

$($

s

$1$

$|$

$$L

$)$

$=$

$0$

$.$

$8$

$9$

$$ P

$($

s

$2$

$|$

$$L

$)$

$=$

$0$

$.$

$1$

$1$

What is the optimal decision strategy if the investor uses the option period to learn more about the resistance from area residents before making the purchase decision?