We are planning for the investment portfolio for a new customer of our consultancy firm.

Analyzing the past investments of the customer, we observed that the utility function is of the type:

$U(x)=(\frac{x}{r_{\text{m}\text{a}\text{x}}-r_{\text{m}\text{i}\text{n}}}{)}^2$

where $r_{\text{m}\text{a}\text{x}}=100$ is the maximum considered revenue and $r_{\text{m}\text{i}\text{n}}=0$ is the minimum revenue.

Question $1(5$ Points$)$

What type of decision maker are we dealing with $($risk averse, risk prone, risk neutral$)?$

Question $2(5$ Points$)$

What is the RP coefficient for this decision maker?

Question $3(10$ Points$)$

What is the maximum price at which we can sell the option in Figure $1$ to our customer? $(10$ Points$)$