Question $1[10$ points$]$ Eric Wong operates a real estate agency in Hong Kong that specializes in

selling properties, which are otherwise hard to sell. He is approached by a client who has three

properties to sell. The client indicates the prices he wishes to receive for these properties as

follows:

Eric would receive a commission of $4\%$ on any of the properties he is able to sell. The client,

however, the following terms specified in a contract:

"Eric, you have to sell Property A$.$ If you can't sell it within a month, the entire deal is off$-$no

commission and no chance to sell the other properties. If you sell Property A within a month, then

I'll give you the commission for it and the option of $($a$)$ withdrawing from the contract at this point;

or $($b$)$ to sell either properties B or C next under the same conditions $($i$.$e$.,$ sell within a month or

no commission on the second property and no chance to sell the third property$).$ If you succeed in

selling the first two properties, you will also have the option of selling the third."

Eric proceeds to analyze the proposal to determine whether or not to accept the contract. He figures

his selling costs and his chances of selling each property at prices set by the client to be:

Eric believes that the sale of a particular property would not make it any more or less likely that

the two remaining properties could be sold. Further, selling costs would have to be incurred

whether or not a particular property is sold, but could be avoided by deciding not to attempt to sell

the property.

Do you think Eric should sign the contract? Draw the decision tree and discuss. Please write down

the optimal decision and corresponding expected profit.