I have $1000 to invest in three stocks. Let R1 be the random variable representing the annual return on $1 invested in stock i. For example, if Ri = 0.12, then $1 invested in stock i at the beginning...

I have $1000 to invest in three stocks. Let R₁
be the random variable representing the annual return on $1 invested in stock i. For example, if R_i
= 0.12, then $1 invested in stock i at the beginning of a year is worth $1.12 at the end of the year. The means are E(R₁) = 0.14, E(R₂) = 0.11, and E(R₃) = 0.10. The variances are Var R₁
= 0.20, Var R₂= 0.08, and Var R₃
= 0.18. The correlations are r₁₂
= 0.8, r₁₃
= 0.7, and r₂₃= 0.9. Determine the minimum-variance portfolio that attains an expected annual return of at least 0.12.