Suppose there are 90 consumers in the market with two goods $x$ and $y$. There are two types of individuals A and B. 60 of the consumers are A and the 30 of them are type B. A consumers have a utility function of $u(x,y) = x^{1/2}y^{1/2}$ and each of them has an income of $m_A$. Type B consumers have a utility function of $u(x,y) = x^{1/3}y^{2/3}$ and each of them has an income of $m_B$.

1. Find the individual demand for A for good $x$ and $y$ as a function of $m_A, p_x$, and $p_y$.
2. Find the individual demand for type B for good $x$ and $y$ as a function of $m_B, p_x$, and $p_y$.
3. Find the market demand for good $x$ as a function of incomes and prices.
4. Find the market demand for good $y$ as a function of incomes and prices.
5. Suppose price of good $x$ is 1 and the price good $y$ is 1. Further suppose $m_A = 20$ and $m_B = 30$. Find the market demand for good $x$ and good $y$ at the given prices and incomes.