A ski resort has always relied on natural snow, which could come in any one

of four levels: heavy, medium, light, or none, with probabilities 0.1, 0.4, 0.3,

and 0.2 respectively. They are now, in July, considering the installation of an

artificial snow-making system before the upcoming season. If installed, the annual

amortized cost would be $40,000. The operating costs of the snow system would

be $0 if the natural snow were heavy, $50,000 if medium, $80,000 if light, and

$110,000 if there were no natural snow. With an artificial snow system, or with

heavy natural snow, they would obtain revenue of $200,000. With no artificial

snow, the revenue would be only $130,000 with medium snow, $70,000 with little

snow, and $0 if there were no snow. Operating costs other than snow-making

would be $45,000 per year (whether artificial or natural snow).

Choosing, before the season begins, to close the operation completely for

the upcoming season, would allow them to rent the land with a rental income

of $20,000.

(a) Solve this problem using a decision tree.

(b) Determine the EVPI by first finding the EV with PI.