Problem $06-17($algo$)$

Amanda has a von Neumann$-$Morgenstern utility function given by $U=\sqrt[\phantom{2}]{M},$ where $M$ is her

income. If she becomes an economics professor, she will make $M=\frac{81}{y}r$ with probability $1.$ If she

becomes an attorney, she will make $M=\frac{900}{y}r$ if she becomes a partner in a Wall Street firm, but

only $M=\frac{49}{y}r$ if she fails to make partner. The probability of her becoming a partner is $0\mathrm{.}2.$ Ellis is an

infallible judge of legal talent. After a brief interview, he can state with certainty whether Amanda will

become a partner. What is the most Amanda would be willing to pay for this information? $($Set up the

relevant equation and solve it$.)$

Instructions: Round your answer to $2$ decimal places.