3. Suppose that you start a small business that uses only capital and labor as inputs. The production function is given by: f (K, L) = K1/2L1/2. The price of a unit of capital is RM4 and the wage is RM1. The price of a unit of output is RM10. (a) Derive expressions for the marginal product of labor and the marginal product of capital. (b) Derive expressions for the optimal amount of labor as a function of output L(y) and the optimal amount of capital as a function of output K(y). (c) Find an expression for total costs as a function of output