$(25$ points$)$ We now have $$500,000$ in assets and are given a choice between investment $1$ and

investment $2.$ With investment $1,70\%$ of the time we increase our asset position by $$300,000,$ and

$30\%$ of the time we decrease our asset position by $$100,000.$ With investment $2,40\%$ of the time we

increase our asset position by $$400,000,$ and $60\%$ of the time we do not change our asset position.

Our utility function for final asset position $x$ is $u(x).$ We are given the following values for $u(x)$:$u(0)=$

$0,u(400,000)=\mathrm{.}5,u(500,000)=\mathrm{.}55,u(800,00)=\mathrm{.}6,u(900,000)=\mathrm{.}85,u(1,000,000)=1.$

a$.$ Based on our utility function how would you classify our risk profile? Explain.

b$.$ Will we prefer investment $1$ or investment $2?$

c$.$ What would our decision be if we were risk$-$neutral?