# Question: how to find the utility numbers at the end of...

###### Question details

How to find the utility numbers at the end of a decision tree? These are the numbers which have been used on the decision tree but I'm unsure what the formula is to get the end utility numbers?

In this example the purple boxed area is what i need help calculating for the following question under it, (not whats already shown just what type of formula should i use to calculate the end utility numbers?)

"A large factory would cost $60 000 to build whereas a small would cost $30 000 to build. Along with that it is said that for every 1000 households that send there recycling to the factories, $800 will be made by the business. There is said to be 50 000, 150 000, 250 000, or 350 000 households which will participate, with probabilities 0.1, 0.35, 0.30 and 0.25.

But the company can choose to buy a report at the price of $10 000 that will either give them a strong (0.4) or weak (0.6) reactions from the households. So for the strong reactions the probabilities are for the 50 000, 150 000, 250 000, or 350 000 households, 0.1, 0.1, 0.4 and 0.4. But for the weak reactions, 50 000, 150 000, 250 000, or 350 000 households have probabilities of 0.4, 0.2, 0.25 and 0.15."