Imagine a representative rm with the following production

Question

Imagine a representative rm with the following production function:

Y = zF(K, N) =zK^α Nd^{(1 - α)} , where 0 < α < 1,

and z represents the total factor productivity, K the amount of capital that the firm owns, and, finally, N the amount of labor it hires. Here, the representative firm is only interested in its protfits, which is defined as

π =Y - wNd .

How would i maximize the following firm, using LaGrange Multipliers?