Question $3[20$ points$]$:$.$ The health care manager is quite concerned about the recent deterioration of a

section of the building that houses her urgent care operations. According to her analyst assistant, four

options merit her consideration: a new building $(A)$; major structural renovation $($B$)$; moderate renovation

$($C$)$; and minor renovations $($D$).$ Moreover, three possible weather conditions could affect the costs of fixing

the building within the next six months. Good weather condition has a probability of $0\mathrm{.}40$ ; moderate weather

with rain has a probability of $0\mathrm{.}35,$ and bad weather has a probability of $0\mathrm{.}25.$

If good weather materializes, $($A$)$ will cost $$215,000$; $($B$)$ will cost $$120,000$; $($C$)$ will cost $$90,000$; and $($D$)$

will cost $$56,000.$ If moderate weather materializes, the costs will be $$255,000$ for $(A)$;$$145,500$ for $(B)$;

$$98,000$ for $(C)$; and $$75,000$ for $(D).$ If bad weather materializes, the costs will be $$316,000$ for $(A)$;

$$214,000$ for $($B$)$; $123,000$ for $($C$)$; and $$119,000$ for $($D$).$

a$.$ Build a payoff table.

b$.$ Draw a decision tree for this problem $($show cost outcomes, probabilities, and EMV for each event node$).$

c$.$ Using expected monetary value $($rollback procedure$),$ which alternative should be chosen?

d$.$ Calculate and interpret the expected value of perfect information.