Question

Decision Tree-Fall Break Shopping Trip Node Node Cost (3) Probabilities Value ($) Flal 12 $2,500.00 13 $2,600.00 14 $2,200.00 15 $2.600.00 16 $2.500.00 17 $2.800.00 18 $2,500.00 19 $2,600.00 20 $1,900.00 21 $3,500.00 22 23 24 $2.500.00 25 $2,800.00 26 $2,100.00 27 $2,600.00 28 $2.200.000 29 $2,600.00 It is the week before fall break and your parents have informed you that your family will be making an overseas trip for a few days. Your parents are undecided as to where the destination will be, but they have refundable tickets on reserve to several different locations: Finland, Sweden, Norway. Greenland, Spain, Rome, Florence, and Monaco. Your parents are astutely watching the weather reports to decide which location to visit. A few days prior to leaving they will cancel the tickets that your family will not be using and be refunded for the unused fickets With the trip approaching fast you decided to go shopping to purchase the necessities to comfortably explore the new countries. You plan to create a decision tree for the costs associated with the clothing, equipment, souvenirs, and food that would be needed for each trip. You will show it to your parents the day before they select the destination, with the goal being to minimize costs and help them decide For this problem, omit the option to do nothing from the decision tree. You are 100% certain that your family will take a trip. As such, the decision to do nothing is irrelevant. The diagram on the following page is the decision tree that you will use to solve the problem. Fill out the table on this page to receive points. Each node (place, decision, etc.) is labeled on the diagram with its corresponding number placed to the top left of its corner. For full credit, all the value and "probability calls must be completed and the destination that you will go to must be written inside of the provided box. There is no need to fill out the shaded cells in the table. Round all numbers and calculations to 2 decimal points. The probability of good weather is 40% Hint: There might be more than one location that you may be heading to. Once you have solved the decision tree, work from left to right until you get a state of nature node and then trace the possible paths to get your answer(s). Which destination(s) might you be heading to?

Answer 1

EV at node 5 ( finland) = 2500x0.4+2600x0.6 =1000+1560 =2560

EV at node 6 ( sweden) = 2200x0.4+2600x0.6 = 2440

Decision at node 2 = sweden with 2440.

EV at node 7 = 2500x0.4+2800x0.6 =2680

EV at node 8 = 2500x0.4+2600x0.6 =2560

Decision at node 3 = Greenland with 2560

EV at node 9 = 1900x0.4+3500x0.6 = 2860

EV at node 22 =2100x0.4+2600x0.6 = 2400

EV at node 23 =0.4x2200+0.6x2600 = 2440

Decision at node 10 = Italy(rome) with 2400

EV at node 11 = 2500x0.4+2800x0.6 = 2680

Decsion at node 4 = 2400 Italy rome

Best decision will be min[ cost at node 2,3 and 4]

which is Italy ( Rome) which has the lowest cost of 2400