Suppose utility is governed by the following function, U(x)=100(x10)2 and that 0x10. a) Graph this utility function. b) Suppose the individual must choose between two options. The first option is to receive 7 units of x with certainty. The second option is to receive 3 units with probability 1/3 or 9 units with probability 2/3. a. Label the utility of the first option on your graph. b. Demonstrate mathematically that the expected utility of option 2 lies on the chord between u(x=3) and u(x=9). c. Compute the utility of Option 1 and the expected utility of Option 2, and compare. d. Note that the first option, receiving 7 units, is the same as the expected value of the number of units received from Option 2. How many of those 7 units would this individual be willing to give up in order to avoid being given Option 2 in favor of receiving a fixed amount with certainty? (Assume that x can be split into fractional numbers of units.) Suppose utility is governed by the following function, U(x)=100(x10)2 and that 0x10. a) Graph this utility function. b) Suppose the individual must choose between two options. The first option is to receive 7 units of x with certainty. The second option is to receive 3 units with probability 1/3 or 9 units with probability 2/3. a. Label the utility of the first option on your graph. b. Demonstrate mathematically that the expected utility of option 2 lies on the chord between u(x=3) and u(x=9). c. Compute the utility of Option 1 and the expected utility of Option 2, and compare. d. Note that the first option, receiving 7 units, is the same as the expected value of the number of units received from Option 2. How many of those 7 units would this individual be willing to give up in order to avoid being given Option 2 in favor of receiving a fixed amount with certainty? (Assume that x can be split into fractional numbers of units.)