Question

please show answers clearly

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 Payoff 3 Payoff 4 0.30 0.50 Payoffs Alternative A Payoff 6 0.20 1/3 1/3 1/3 Payoff 7 Payoffs Payoff 9 Alternative B 5 0.30 Payoff 10 0.50 Payoff 11 0.20 Payoff 12 1/2 6 Payoff 13 1/2 Payoff 14 3 7 Payoff 1 $ 2 6 4 -4 5 6 6 7 8 9 10 11 12 13 14 7 8 5 8 4 4 5 6 5 3

Answer 1

a) The Answer:- value of node 4 es (using Picture) At Node 4: It is Combination of Node I and pay off at a Node 1 is - - (payoff 1 + pay off at payoff 3) As per the table using values from pay off 1,2,3 = 6,6,5 (6+6+6) = 12 12 - 5.67 (approx) value of Node 4= pay off = Nodelt payoff 4) = 5.67 + (-4) Value at node 4 = 1.67. (in I decimal place) = 1.7 (approx.) - 5.666 . Value 1.67

b) The value at hode 8 is Node 8 is Combination of node 5 and 6 and pay off at Node 8 can be defined node to pay off. leto 11 (0.5 * pay off 11) +0.3 Node 5) + fo.Q Node 6) Node 5 = Node 2 + pay off 10 1/3 (pay off 7, 8, 9.) + 15 $(-3 + 8 + 8) +5 4+5 १ Node 5 = 9 Same node to = node 3+ pay off 12 Payoff á (134) + pay off 12 1 ( 4 + 5 + 4 1! 8.5 (945) 3 Node 6= 8.5

i Node 8 - 0.3 x Node 5 + 0.5 x pay off! + 0.2 * Node 6 - (0.349) (0.5*8)+ 6.2 x 8.6) 0 00 8.4 Value at node 8 = $8. 4 C Best alternative would be alternative Vale at node A &$1.7 value at node 8 $8.4 workings based Node 7 - (0.3 * Node 4) + (0.5 x pay off 5) + (0.2 x payoff6) Node 7 = (0.3 * 1, 7) + (0.5*6) + (0. 2* =) 0.51 + 3 + 1.4 -$4.91 - 4.9 based on above Best alternative would be alternative B because Node 8 has higher value is $8.4 vis-avis that of Node 7 which has value of $4.9