3. (5%) Suppose that a representative firm in a perfectly competitive industry has the production function $f(x_1, x_2) = \min\{x_1, x_2\}^n$ with $0 < \alpha < 1$, where $x_1$ and $x_2$ are the amounts of inputs 1 and 2, respectively. Denote $w_1$ and $w_2$ the prices of inputs 1 and 2, respectively. Suppose that this firm chooses the amounts of inputs 1 and 2 to minimize its costs for producing $y$ units of output. The long run cost function of this firm is _(3a)_ and the long-run supply function of this firm is _(3b)_.