6 As in Problem 5, assume that we must determine the percentage of our money that is invested in stocks x and y. A choice of a and b is called a portfolio. A portfolio is efficient if there exists no other portfolio whose return has a higher mean return and lower variance, or a higher mean return and the same variance, or a lower variance with the same mean return. Let x be the mean return on stock x and y be the mean return on stock y. Consider the following NLP:

Suppose that 1 > c > 0. Show that any solution to this NLP is an efficient portfolio.

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max z = c[ax + by] s.t. -(1c)[avar x+ bvar y +2abcov(x, y)] a+b=1 a, b 0 rx