# Decision Tree

*label*Statistics

*timer*Asked: Apr 16th, 2017

**Question description**

A local fashion retailer is seeking a new retail outlet in the neighbourhood estate. The property agent recommended two possible sites. One of the sites (Site A) is near to the bus interchange and is relatively small, while the other site (Site B) is further away but has a larger floor area.

If the retailer opens the store at Site A and demand is good, the store will generate an annual profit of $200,000. If demand is low, the retailer will lose $40,000 per annum. If the retailer opens at Site B and demand is high, the store will generate an annual profit of $320,000, but the store will lose $120,000 per annum if demand is low. The retailer also has the option of not opening the new retail outlet. The retailer believes that there is a 55 percent chance that demand will be high.

The retailer is offered a market research study by the property agent. The probability of a good demand given a favourable study is 0.85 while the probability of a good demand given an unfavourable study is 0.1. There is a 70 percent chance that the study will be favourable.

(a) Determine, using the decision tree approach, whether the retailer should purchase the market research study. Show the decision tree and compute the expected values for all relevant nodes.

(b) Determine the maximum amount the retailer would be willing to pay for this study.