Question

Consider the following decision tree in which the probabilities are shown after each chance node and PW values are given for each terminal node. For full credit, you need to provide a detailed solution. (a) What decision should be made? (b) What is the expected value of the best decision? 0.2 - 05– 15.000 12.00 - 16.000 12.000 Pack 22 11.000 7 4 .000

Answer 1

SOLUTION:-

A).

In this part we take our decision on the basis of the expected value of every pick.

Our decision should be C2 OR PICK Y because it gives more payoff.

The decision should be make on the basis of Expetrel

Exp (C1) = 0.2 (15000) + 0.5 (12000) + 0.3 (9000)

= 3000 + 6000 + 2700

= 11,700

Exp (C2) = 0.4 (36000) + 0.6 (8000)

= 14400 + 4800

= 19200

Exp (c3) = 0.3 (-10,000) + 0.7 [ .2 x 12000 + .8 x 9000 ] + 0.7 [ 0.3 (14000) + (.7) 4000 ]

= -3000 + 0.7 [ 2400 + 7200 ] + 0.7 [4200 + 2800 ]

= -3000 + 6720 + 4900

= 8620

We should choose 'Y' at ' $\mu$ '

we should choose C2

B).

The expected value of C2 or PICKY is 19200.

Exp (Y) or Exp (C2) = 0.4 (36000) + 0.6 x 8000

= 14400 + 4800

= 19,200

Exp(Y) or Exp(C2) = 19,200

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