Finding the supply function from a production function

Question

Given the production function $f(z_1,z_2)=\sqrt{az_1+bz_2}$ where $z_1$ and $z_2$ are inputs, $a$ and $b$ are scalars; find the supply function: $y(p)$ output as a function of prices, and the profit function: $\pi(p)$ profit as a function of prices. I tried setting it up as a profit maximizing problem but everything cancels out and you can't find an optimal bundle of $z_1$ and $z_2$.