Need help with macroecon please

Production model (15 points). Consider the following production function Y = AK1/3L1/2 Suppose capital supply is I? and labor supply is Z. Denote product price by P. Denote the rental rate of capital by 'r. And we set the wage rate as the numeraire, i.e. w = 1. (a) Write down rm's prot function. (b) Derive the capital demand function and the labor demand function. (C) Show that the prot of the rm is not zero