Two states with probabilities $($w$0,0\mathrm{.}0)$Example

The agent with wealth $(w_0,0,0)$ has access to asset market

$r=\left[\begin{array}{cc}1& \frac{1}{2}\\ 1& 2\end{array}\right]$

Two states with probabilities $(,1-)=(\frac{1}{2},\frac{1}{2}),$ prices of assets $q=(1,\frac{3}{4}),$ vNM utility

$v(y)=ln(y).$ Solve optimal portfolio $(a_1,a_2).$