Below is the augmented portion of the earlier decision tree. (in other words, th

Question

Below is the augmented portion of the earlier decision tree. (in other words, there is a decision node Before the Market research brace, joining this branch to the tree in problem 2, as in class.) a. What is the expected value for the decision at node 4? b. What decision should be made at node 2? Explain your reasoning. c. What is the expected value for the decision at node 5? d. What decision should be made at node 3? Explain your reasoning. e. What is the expected value for the decision at node 1?

Explanation / Answer

Part (a)

At node 4, possibilities are: high demand with a probability of 0.85 and pay-off of 2650 and low demand with a probability of 0.15 and pay-off of 650.

So, expected value at this node = (0.85 x 2650) + (0.15 x 650) = 2350 ANSWER

Part (b)

At node 2, decision options are: build complex with an expected pay-off of 2350 as evaluated in Part (a) or sell with pay-off 1150.

Since 2350 > 1150, decision is: build complex ANSWER

Part (c)

At node 5, possibilities are: high demand with a probability of 0.225 and pay-off of 2650 and low demand with a probability of 0.775 and pay-off of 650.

So, expected value at this node = (0.225 x 2650) + (0.775 x 650) = 1100 ANSWER

Part (d)

At node 3, decision options are: build complex with an expected pay-off of 1100 as evaluated in Part (c) or sell with pay-off 1150.

Since 1150 > 1100, decision is: sell ANSWER

Part (e)

At node 1, possibilities are: forecast high with a probability of 0.6 and pay-off of 2350 [vide Part (b)] and forecast moderate with a probability of 0.4 and pay-off of 1150. [vide Part (d)]

So, expected value at this node = (0.6 x 2350) + (0.4 x 1150) = 1870 ANSWER

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