Given is a Decision Tree Diagram. The Payoffs 1-14 are given in the table below. Answer questions a, b, and c.
Payoff |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
$ |
7 |
-4 |
5 |
2 |
7 |
4 |
5 |
-3 |
5 |
3 |
3 |
2 |
8 |
6 |
a) The value at node 4 is
b) The value at node 8 is (in 1 decimal place)
c) The best course of action or decision is to select
alternative
a)
Value at node 1 = 7*1/3+(-4)*1/3+5*1/3 = 8/3 = 2.67
Value at node 4 = Maximum of Value at node 1 or Payoff 4 = Maximum of 2.67 or 2
= 2.67
----------------------------------------------------------
b)
Value at node 2 = (5-3+5)*1/3 = 7/3 = 2.33
Value at node 5 = Max of 2.33 or payoff 10 (3) = 3
Value at node 3 = (8+6)*1/2 = 7
Value at node 6 = Max of 7 or payoff 12 (2) = 7
Value at node 8 = 0.3*Value at node 5 + 0.5*Payoff 11 + 0.2*Value at node 6
= 0.3*3+0.5*3+0.2*7
= 3.8
----------------------------------------------------------
c)
Value at node 7 = 0.3*Value at node 4 + 0.5*Payoff 5 + 0.2*Payoff 6
= 0.3*2.67+0.5*7+0.2*4
= 5.1
Value at node 9 = Max of Value at node 7 (5.1) or Value at node 8 (3.8)
= Value at node 7 (5.1)
Therefore, the best course of action is to select alternative A
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Additional Work:
Complete decision tree showing the payoffs and Values at each node is following:
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