John invests one unit of money in two business projects; an amount of goes to the

John invests one unit of money in two business projects; an amount of α goes to the first, and 1−α goes to the second. For i = 1, 2, let X_i be the (random) return (per $1) of project i. It is known that the means of X₁ and X₂ are the same. The variances σ²_i = Var{X_i} and ρ = Corr{X₁,X₂} ≠ ±1 are known. Show that the mean return does not depend on α and find an α minimizing the variance of the return.