Part I. In order to compute the value at each of the following nodes, you would

Question

Part I. In order to compute the value at each of the following nodes, you would need to write a mathematical expression to compute the value. For the following questions, you are asked to write the mathematical expression to compute the value at each of the following nodes. Reminder! You are required to write the mathematical expression only, not the resulting computation value. You will be asked to enter the resulting value in Part II.
a) The mathematical expression to compute the value at node 1 is  
b) The mathematical expression to compute the value at node 3 is  

Part II. What is the resulting computation value at each of the following nodes.
c) The value at node 1 is  (in 1 decimal place)
d) The value at node 3 is  (in 1 decimal place)
e) The value at node 4 is  
f) The value at node 6 is  

Part III. Use the information in the tree diagram, Part I, and Part II to answer the following questions.
g) The mathematical expression to compute the value at node 7 is  
h) The value at node 7 is  (in 1 decimal place)

Part IV. Solve and analyze the entire decision tree diagram to select the best alternative.
i) The value at node 8 is  (in 1 decimal place)
j) The best alternative is to select the alternative

Payoff 1 2 3 4 5 6 7 8 9 10 11 12 13 14 $ 5 -2 5 2 9 2 5 -5 3 4 4 -3 7 6 1/3 1/3 1/3 Payoff 1 PayOff 2 PayO ff 3 Pa yO ff 4 0.50 Payo ff 5 Alternative A 0.20 Payoff 6 9 1/3 1/3 1/3 PayOff 7 PayO ff 8 Payoff 9 Alternative B 0.30 PayOff 10 0.50 8 PayO ff 11 0.20 PayOff 12 Pa yOff 13 PayOff 14 6 1/2 1/2

Explanation / Answer

a,c,c,d) value at node1: Mathematical expression:

=1/3(payoff 1) + 1/3(payoff2) +1/3(payoff3)

=8/3

value at node 3: Mathematical expression:

=1/2(payoff 13) +1.2(payoff 14)

=13/2

e)1/2(8/3) 1/2(payoff4) = 4/3 +2 = 10/3

d)1/2(13/2) + 1/2(payoff12) = 13/4 - 3 = 1/4

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