Job Offers Decision Tree Problem I

You are currently in the process of interviewing for jobs. Current information is shown below.

Job A has a starting salary of $$80,000.$ You have an interview scheduled to occur $7$ days from now. If you get a job offer from that interview, it will come immediately $($on day $7).$ You estimate the probability that you will be offered the job to be $0\mathrm{.}70.$ If you receive an offer for Job A$,$ you will need to give an answer by day $11.$

Job B has a starting salary of $$77,000.$ You have already interviewed and received a job offer. You need to give them an answer by day $5.$

Other information in the table below has similar interpretations. You should assume that if you pass the deadline for accepting a job offer, you lose the opportunity to accept the job. If you ac cept a job, you will not attend any subsequent interviews or entertain any other job offers.

Job Salary P $($Offer$)$ Interview Deadline

A $$80,0000\mathrm{.}7711$

B $$77,000$ na offered $5$

c $$75,000$ na offered $10$

D $$55,000$ na offered $17$

E $$90,0000\mathrm{.}11215$

Draw $($by hand$)$ the decision tree that represents this multi$-$stage decision scenario. Your tree should reflect the sequence of decisions you need to make, as well as what is known vs$.$ not known at the time the decision needs to be made. $($Outcomes for interviews that are still in the future are unknown.$)$

Each decision node should have branches for all of the options that should be considered at that point in time. $($Do not omit branches simply because you would not choose that alternative under the current information.$)$ If you have already passed the deadline for accepting a job offer, accepting that job is no longer an alternative. If you have not $($including not yet$)$ received a job offer, accepting that job is not $($yet$)$ an alternative.

The tree should be complete with all branch values, branch probabilities, and terminal values. $($The only branches that should have non$-$zero branch values are those that represent accepting a job. Each of the terminal values will then be the salary for the one job that is accepted.$)$