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Problem 3: You have access to two investmentopportunities. Mutual Fund A, which promises 20% expected returnwith a variance of 0.36, and Mutual Fund B, which promises 15%expected return with a variance 0f 0.12. The correlation betweenthe two is 0.084.2. In addition to the funds A and B in the previous question,now you decide to include fund C to your portfolio. Its expectedreturn is 10%, its variance 0.0625, its correlation with A is0.1050 and its correlation with B is 0.07. You want to achieve anexpected return of 16% on your portfolio, with the minimum possiblerisk (measured by the standard deviation). Derive analytically(that is, without the help of solver, but through calculus) theweights of such desired portfolio, and its standard deviation.