General equilibrium regarding on U= max(ax,ay) + min(x,y) Please kindly instruct me on solving the following in a general equilibrium framework with standard budget constraint,
$$ u^{1}\left ( x  \right )= max\left [ \frac{x_{1}}{10}, \frac{x_{2}}{10}\right ]+ min\left [ x_{1},x_{2} \right ] $$
, with $e^{1} = (10,10)$


What would this consumer demand at prices $p = (\frac{3}{4}; \frac{1}{4})$?


Given the other two consumer utilities

$$u^{2}\left ( x  \right )= x_{1}^{\frac{2}{5}}x_{2}^{\frac{3}{5}} $$

$$u^{3}\left ( x  \right )= x_{1}^{\frac{3}{5}}x_{2}^{\frac{2}{5}}$$
, with $e^{2} = (4,6)$ , $e^{3} = (4,4)$ 


Find one Walrasian equilibrium (and determine both equilibrium prices and the equilibrium allocation).


I have completely no idea how to start with it...

Thank you!
Let us name three consumers A, B and C, and two goods X and Y. Equilibrium price vector $(p_x, p_y=1)$ and allocation $((x_A, y_A), (x_B, y_B), (x_C, y_C))$ satisfy the following:

Optimality Conditions (Allocation must solve the utility maximization problem of the three consumers, i.e. it must lie on the demand functions)


$(x_A, y_A) = \begin{cases} \left(\frac{10p_x+10}{p_x}, 0\right)  &amp; \text{if } p_x \leq \frac{1}{10}  \\ \left(10,10\right) &amp; \text{if } \frac{1}{10} \leq p_x \leq  10 \\ \left(0, 10p_x+10\right) &amp; \text{if } p_x \geq 10\end{cases} $
$(x_B, y_B) = \left(\frac{2(4p_x + 6)}{5p_x}, \frac{3(4p_x + 6)}{5}\right)$ 
$(x_C, y_C) = \left(\frac{3(4p_x + 4)}{5p_x}, \frac{2(4p_x + 4)}{5}\right)$


Feasibility Conditions


$x_A + x_B + x_C = 18$
$y_A + y_B + y_C = 20$


Solving the above gives price vector $(p_x, p_y) = (1.2, 1)$ that supports the allocation $((x_A, y_A), (x_B, y_B), (x_C, y_C)) = ((10, 10), (3.6, 6.48), (4.4,3.52))$ in equilibrium.