Question

QUESTION 3 Given is a Decision Tree Diagram. The Payoffs 1-14 are given in the table below. Answer questions a, b, and c. 1/3 1/3 1/3 PayOff 1 PayOff 2 Pa yoff 3 PayOff 4 0.3 0.50 Payoff 5 Alternative A 0.20 PayOff 6 9 1/3 1/3 1/3 Pa yOff 7 Pa yoff 8 PayOff 9 Alternative B 0.30 PayOff 10 0.50 PayOff 11 0.20 PayOff 12 Pa yOff 13 PayOff 14 1/2 6 3 1/2 Pavoff 1 2 3 4 5 678 9 10 11 |12113 14 S34273455845 94 a) The value at node 4 is b) The value at node 8 is c) The best course of action or decision is to select alternative (in 1 decimal place)

Answer 1

a) Value at node 4 = Value at Node 1 + Payoff 4 = [(1/3)*[Payoff 1 +Payoff 2+Payoff 3]]+Payoff 4

Value at node 4 = [1/3*(-3+4+6)]+2 = 13/3 = 4.33

b) Value at node 8 = [0.3*node 5]+[0.5*Payoff 11]+[0.2*node 6]

Value at node 8 = [0.3*(node 2+Payoff 10)]+[0.5*(4)]+[0.2*(Payoff 12+node 3)]

Node 8 = [0.3*((1/3)*(-4+5+5)+8)]+2+[0.2*(5+(1/2)*(9+4)))] = 3+2+2.3 = 7.3

Value at node 8 = 7.3

c) To find best course of actions or decision, we need to calculate value at node 7 as well.

Node 7 = [0.3*node 4]+[0.5*Payoff 5]+[0.2*Payoff 6] = [0.3*13/3)+[0.5*7]+[0.2*3] = 2.8+1+0.8 = 5.4

Value at node 7 = 5.4

Hence, the best alternative is to Alternative B with a payoff value of 7.3