1/3 1/3 1/3 Payoff i Payoff 2 Payoff 3 Payoff 4 0.50 Payoff 5 0.20 Payoff 6 1/3

Question

1/3 1/3 1/3 Payoff i Payoff 2 Payoff 3 Payoff 4 0.50 Payoff 5 0.20 Payoff 6 1/3 1/3 Payoff 7 Payoff a Payoff 9 Given is a Decision Tree Diagram. The Payoffs 1-14 are given in the table below Altematve B Payoff 1 0.50 Payoff 11 0.20 Payoff 12 Payoif 13 Payoff 14 1/2 1/2 ?) The value at node 1 is b) The value at node 3 is c) The value at node 5 is d) The value at node 7 is e) The value at node 8 is f) The best course of action or decision is to select alternative in 1 decimal place) in 1 decimal place) in 1 decimal place) in 1 decimal place) (in 1 decimal place)

Explanation / Answer

a) Value at node 1 = (1/3)*6+(1/3)*10+(1/3)*(-6) = 10/3

b) Value at node 3 = (1/2)*4+(1/2)*7 = 11/2

c) Value at node 5 = Value at node 2 + Value from payoff 10 = [(1/3)*(-9)+(1/3)*8+(1/3)*(-5)]+8 = 6

d) Value at node 7 = (Value at node 4)*0.3 + (Value from payoff 5)*0.5 + (Value from payoff 6)*0.2 = [(10/3)+(3*3)]*0.3+0.5*8+0.2*4= 17/2

e) Value at node 8 = (Value at node 5)*0.3 + (Value from payoff 11)*0.5 + (Value from node 6)*0.2 = (6*0.3)+(-6)*0.5+(5+(1/2)*4+(1/2)*7) = 9.3

f) The best course of action can be decided based on values alternative A and alternative B-

Alternative A value = Value at node 7 = 17/2 = 8.5

Alternative B value = Value at node 8 = 9.3

Hence, Alternative B is best.

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