Problem $3(38$ ?points $)$

Roubina was the proprietor of a real estate firm specializing in investment properties in the Ottawa area.

Roubina's business had done well during the real estate boom in the Ottawa area. Just recently a

prospective client who held land for speculation offered Roubina an exclusive listing property subject to

some special restrictions which the client felt would ensure that Roubina would market the property with

due diligence. The selling price of the property is $ $1,000,000($ i $.$ e $.,$ ?one million dollars $).$ ?Roubina would

receive a commission of $5\%$ ?for selling the property.

Also, Roubina agrees to market the property and if she fails to sell within two months that will cancel her

right to sell that property. She assessed the selling costs from her previous experience in advertising and

selling similar properties in the past. These costs would be incurred even if no sales were made. Of

course, these costs would not be incurred if Roubina refused to list the property. Roubina also

assessed her chances of sale based upon her historical experience with similar parcels at the same general

price level. The promotional expense is $ $5000,$ ?and the probability of sale $($ prior probability $)$ ?is $0\mathrm{.}5.$

Roubina also decided to consider the possibility of doing a very quick market survey to get a better idea

of the chances of a sale. The cost of such a survey would be $ $2000.$ ?Based upon past experience, Roubina

is able to estimate that in the cases of successfully selling $($ within two months $)$ ?a property, there were $90\%$

of these cases that the market survey indicated a strong real estate market, whereas in the cases of failing

to sell $($ within two months $),$ ?there were $70\%$ ?of these cases that the market survey indicated a weak real

estate market. Roubina hired a recent

B $.$ Com. Graduate to perform a full analysis of her decision problem.

a $)$ ?Use the likelihoods $/$ conditional and prior probabilities to calculate all the posteriors $/$ revised

probabilities. Show your work $/$ calculations $.(14$ ?points $)$

Round the probabilities to three decimal points.

b $)$ ?Draw and solve the decision tree for this entire problem to determine the optimal decision

strategy that Roubina should follow. $($ Show your work $/$ calculations $).$ ?Verbally communicate the

decision strategy. $(21$ ?points $)$

c $)$ ?Find the Expected Value of Sample information $($ EVSI $),$ ?which is the maximum amount that

Roubina is willing to pay for the survey. $(3$ ?points $)$