Mary is considering opening a new grocery store in town. She is evaluating three sites: downtown, the

Question:

Mary is considering opening a new grocery store in town. She is evaluating three sites: downtown, the mall, and out at the busy traffic circle. Mary calculated the value of successful stores at these locations as follows: downtown, $250,000; the mall, $300,000; the circle, $400,000. Mary calculated the losses if unsuccessful to be $100,000 at either downtown or the mall and $200,000 at the circle. Mary figures her chance of success to be 50% downtown, 60% at the mall, and 75% at the traffic circle.

(a) Draw a decision tree for Mary and select her best alternative.

(b) Mary has been approached by a marketing research firm that offers to study the area to determine if another grocery store is needed. The cost of this study is $30,000. Mary believes there is a 60% chance that the survey results will be positive (show a need for another grocery store). SRP = survey results positive, SRN = survey results negative, SD = success downtown, SM = success at mall, SC = success at circle, SD = don’t succeed downtown, and so on. For studies of this nature: P(SRP | success) = 0.7; P (SRN | success) = 0.3; P (SRP | not success) = 0.2; and P (SRN | not success) = 0.8. Calculate the revised probabilities for success (and not success) for each location, depending on survey results.