Question

Question Completion Status: Given is a Decision Tree Diagram. The Payoffs 1-14 are given in the table below. Answer questions a, b, and e. 1/3 1/3 1/3 Payoff 1 Payoff 2 Payoff 3 0.30 Payoff 4 0.50 Payoff 5 Alternative A 0.20 PayOff 6 9 1/3 1/3 PayOff 7 Payoffs Payoff 1/3 5 Alternative B 0.30 Payoff 10 0.50 8 Payoff 11 0.20 Payoff 12 1/2 6 Payoff 13 1/2 Payoff 14 Click Save and submit to save and submit. Click Save All Antall answers

Answer 1

(i) value of node 1 = 1/3* ( sum of payoff 1, 2 and 3) =7/3

Value at node 4 = max [ payoff 4, value of node 1] = [2,7/3] =7/3

(ii) Value of node 2 = 1/3 *[ sum of payoffs of 7,8,9] = 1/3 [ -3-4+8]=1/3

Value of payoff 10=6

Value of node 5 = Max [ value of node 2, value of payoff 10]= [ 1/3.8]=8

Value of payoff 3 = 1/2 * ( value of 13 + value of 14] = 0.5 *(7+5) =6

Value of payoff 12=-4

Value of node 6 = max [ Value of payoff 12, Value of node 3] = Max [ 4. 6]=6

Valur of node 8 = 0.3*value of payoff at node 5 + 0.5* payoff 11+0.2*Value of node 6

=0.3*8+0.5*(-5)+0.2*6 = 1.1

Value of node 7 = 0.3*value at node  4 + 0.5*payoff 5+0.2*payoff at node 6

= 0.3*7/3 + 0.5*7+0.2*6 = 5.4

Alternative 1 is best option as it has higher value