A company that produces a certain item had a profit this year of 150 million, the manager of the company wants to increase the profit by introducing a new item similar to the previous one. For this he can hire a consulting firm that does market research, which charges him 20 million, the possible results of the demand are: high (a), regular (r) and low (b). Based on the consulting firm's history, the following table of forecast errors is available.

The table is interpreted as follows, if the demand was high (A) and it was predicted to be fair (r), the consulting firm fails in 5% of the cases. Thus, for the other situations.

If the demand was high and it was predicted high, the consultancy was correct in 95% of the cases (it failed in 5%), If the demand is regular and it was predicted to be regular, the consultant is correct in 90% (it failed in 10% ), of the cases and finally if the demand is low and the consultancy was predicted to be low, the consultancy is correct in 85% (it failed in 15%), of the cases.

The administrator has estimated the following for the three possible types of demand in the event that the new article is introduced:

High demand (A), with P (A) = 0.3 and a profit of 300 million.

Regular demand (R), with P (R) = 0.5 and a profit of 100 million.

Low demand (B), with P (B) = 0.2 and a profit of -100 million.

What will be the best decision that the administrator of the company can make? Use the expected value criterion.

Make the tree diagram with the excel decision tree plugin

Calculate the posterior probabilities and expected values ??of each node in the tree

What is the optimal decision?