maximizing leontief-type utility function
You can re write $u(x, y)$ as
\begin{eqnarray*} u(x, y) = \begin{cases} ax + y &amp; \text{ if } x &gt; y\\ ay + x &amp; \text{ if } x \leq y\end{cases} \end{eqnarray*} 

When one plot the indifference curves, this is how they will look:



Here $\mu_1 &gt; \mu_2 &gt; \mu_3$.