INSTRUCTIONS: DRAW THE TREE, LABELING EACH BRANCH, INCLUDING PROBABILITIES IF APPROPRIATE. PUT THE PAYOFFS AT THE END OF THE BRANCHES, CALCULATE ALL THE EXPECTED VALUES, AND PUT THEM IN TREE AS WELL.

As head of Human Resources, you are in control of hiring new personnel. For a typical position opening, you must decide whether to search inside the company, outside the company, or simply do no search at all. No search means you don't fill the position. For the current opening, you estimate that not filling the position will cost the company $$20,000$ in lost efficiency. If you decide to do an outside search, you must decide whether to do just a local search, or a national one. You estimate there is an $80\%$ chance of a local search turning up a qualified person for the current opening $($if you don't find anyone, you're out the $$3,000$ you have spent and you have to start over$),$ while a national search has a $90\%$ chance of finding someone qualified $($losing $$9,000$ if you don't find anyone qualified, and you start over$).$ If you find someone qualified in the national search, there is a $60\%$ chance they will accept your offer, ultimately being worth $$100,000$ to the company, but if they reject your offer you start over after losing $$10,000.$ For the local search, there is a $90\%$ chance a qualified person would accept your offer, being worth $$105,000$ to your company, but if they turn you down you are out $$4,000.$ If you choose to search inside the company, there is a $60\%$ chance of finding a qualified person. If no qualified person is found, there is an $80\%$ chance you can find a person who can be trained to fill the position. If no trainable person is found, you are out $$3,000$ and you start over. Even if a trainable person is found, you must decide whether or not to make them an offer $($there might be trouble over taking a person from another department$).$ If you choose not to make an offer, you are out $$5,000$ and you start over. If you choose to make an offer, there is a $75\%$ chance of it being accepted, which is worth $$120,000$ to the company, whereas a rejection of your offer would leave out $$6,000$ and starting over. If the inside search turns up a qualified person, you must decide whether or not to make them an offer $($no offer leaves you out $$2,000$ and starting over$).$ There is a $50\%$ chance a qualified person would accept your offer, being worth $$150,000$ to the company, but a rejection of your offer would cost you $2,500,$ and you start over. Note: starting over is the end of branch, with whatever costs have been accrued to that point as the payoff.