Suppose that a decision maker$$s risk attitude toward monetary gains or losses x given by the utility function u left parenthesis x right parenthesis equals left parenthesis $10000$ plus x right parenthesis to the power of bevelled $1$ half end exponent $.$ Suppose that a decision maker has been given a lottery ticket for free. Suppose that the lottery winning is $$500,000,$ and the chance of winning is one in a thousand. What is the minimum price that the decision maker would be willing to sell the ticket for?

$$1\mathrm{.}23$

$$123\mathrm{.}2$

$$12\mathrm{.}23$

$$122\mathrm{.}3$

$$142$

$$1\mathrm{.}42$