Please help me answer the question below

1. 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)=5x _ Unfortunately, we don't know Jane, the youngest kid's utility function yet. a) Given their utility functions, what are Macy and Theodore's u-values if they can get each of the following monetary payoffs for sure (fill your answers in the table)? Dollar Value ($) Macy's u-value Theodore's u-value 10 20 30 50 60 70 80 90 100 b) Draw the utility curves for Macy and Theodore (you can either draw 2 curves separately or on the same graph). Label them carefully. c) Now both are facing the following uncertain deal (Deal A). Find Macy's and Theodore's expected u-values of Deal A. Deal A $100 0.25 0.75 SO d) What are Macy's and Theodore's u-values of the certain equivalents of Deal A? What are their certain equivalents (CE) for Deal A? f) Compare the values of CE you found in the previous question. Explain why there is such difference in their CEs for the same deal g) Jane is also interested in the deal. Even though we don't know her utility function, we are lucky to have her u-value for each dollar amount as shown in the following table.Dollar Value ($) Jane's u-value 0.00 10 2.53 20 7.16 30 13.15 40 20.24 50 28.28 60 37.18 70 46.85 80 57.24 90 58.31 100 80.00 As we don't know her utility function, we don't know exactly Jane's certain equivalent for the deal like we do in the cases of Macy and Theodore. But what can we say about the range of her certain equivalent (choose one of the options below)? Explain why (Hint: you need to find her expected u-value for Deal A first and then deduce the range for her CE from the above table). i. Between $10 and $30 ii. Between $30 and $50 iii. Between $50 and $100 iv. Over $100 h) Three of them is now facing another deal (Deal B). Deal B Dollar Value $50 0.3 $20 0.2 $10 0.5 Find the (range of) certain equivalent for Macy, Theodore, and Jane for the new deal. ) Among the two deals (A and B), what is the best deal for Macy, Theodore and Jane, respectively? i) 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? k) Draw a decision tree which characterizes the decision situations Macy was facing (see Figure 10.15/pg. 208 in the textbook for reference). 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)