Liz has a small shop where she sells shirts and other tops. Unexpectedly the local high school basketball team has reached the state semi-finals. A few days before the game a supplier offers her a consignment of either 500 or 1000 of the team's shirts at a good price. She must make a decision right away. If the team reaches the final, (a 60% chance according to the sportscasters), Liz will be able to sell all of the shirts at a profit of $10 each. If they do not reach the final and she has ordered 1000, she will not sell any this season, but could store them and sell them at a profit of $5 each next season unless the team changes their logo in which case she makes only $2 per shirt. The probability of changing the logo is 75%. Rather than storing the shirts, she could sell them to a close-out chain for a profit of $2.50 per shirt. If Liz orders 500 shirts and the team reaches the final, she will be able to sell all the shirts at a profit of $10 each. If they do not make the final and she has ordered 500, she will not have the option of selling to the discount chain and could only sell them the next season at a profit of $5 each if the logo does not change and at a profit of $2 if the logo changes Construct the decision tree for this situation What course of action to we recommend to Liz and why?
This solution is comprised of a detailed explanation of the various aspects of Decision Tree as it pertains to the given problem and provides students with a clear perspective of the calculations and underlying concepts.