x₁, x₂ and x₃ are the proportions of an investor's portfolio held in three assets. The means of the previous returns are m₁, m ₂ and m₃; and the variances of the earlier returns are s₁², s ₂² and s₃²; the co-variances are s₁₂, s₁₃ and s₂₃.

(a)Define the expected return on the portfolio E(R_p) and the portfolio variance s _p².

(b)Define the LaGrange function that would allow the investor to use the previous asset returns to select a portfolio to minimize s _p² for an expected portfolio return of E(R_p*).

(c)Find the first order conditions needed to solve for x₁, x₂ x₃ and l.

Note: You are not required to solve for x₁, x₂ x₃ and l, you are simply being asked for the first order conditions.