The Lamberts family have three children: Macy, Theodore, and Jane. Each of them has different attitude towards money. In particular, Macy's utility function is u(x)=6+0.5x and Theodore's utility function is U(x)=5x1/2. Unfortunately, we don't know Jane, the youngest kid's utility function yet. Jane is also interested in the deal. Even though we don't know her utility function, we are lucky to have her u-value for each dollar amount as shown in the following table. Deal A Deal B Dollar Value $50 $100 0.25 0.3 $20 0.2 $10 0.75 $0 0.5 Dollar Value ($) 0 10 20 30 40 Jane's u-value 0.00 2.53 7.16 13.15 20.24 28.28 37.18 46.85 57.24 68.31 80.00 50 60 70 80 90 100 Suppose their parents decide to give them $23 with the condition that they have to give up any deal they chose above (let's call it Deal C). Who among them should walk away with $23...Draw a decision tree which characterizes the decision situations Macy was facing. Instructions: Boxes represent decision alternatives (i.e., Deal A, Deal B, and Deal C) Ovals/circles represent each state of nature for each deal. Record probabilities, payoffs, and u-value for each branch of the tree. Record u-value and certain equivalents for each deal (note that CE for Deal C is $23). The Lamberts family have three children: Macy, Theodore, and Jane. Each of them has different attitude towards money. In particular, Macy's utility function is u(x)=6+0.5x and Theodore's utility function is U(x)=5x1/2. Unfortunately, we don't know Jane, the youngest kid's utility function yet. Jane is also interested in the deal. Even though we don't know her utility function, we are lucky to have her u-value for each dollar amount as shown in the following table. Deal A Deal B Dollar Value $50 $100 0.25 0.3 $20 0.2 $10 0.75 $0 0.5 Dollar Value ($) 0 10 20 30 40 Jane's u-value 0.00 2.53 7.16 13.15 20.24 28.28 37.18 46.85 57.24 68.31 80.00 50 60 70 80 90 100 Suppose their parents decide to give them $23 with the condition that they have to give up any deal they chose above (let's call it Deal C). Who among them should walk away with $23...Draw a decision tree which characterizes the decision situations Macy was facing. Instructions: Boxes represent decision alternatives (i.e., Deal A, Deal B, and Deal C) Ovals/circles represent each state of nature for each deal. Record probabilities, payoffs, and u-value for each branch of the tree. Record u-value and certain equivalents for each deal (note that CE for Deal C is $23)