Numerical Optimization - Analytical Questions

Apple and Google have expected returns of 5% and 7% and standard deviations of 10% and 12%. Their correlation is 0.30 and the risk-free rate is 2%. You want to form a portfolio by investing in Apple and Google. Solve for the investment weights that create the optimal portfolio, as defined in each problem below. Assume short selling is not allowed.

1. The portfolio that maximizes the Sharpe ratio.
2. The portfolio that maximizes the risk premium.
3. The portfolio that minimizes the variance.

For each problem above, identify:
1. Objective function
2. Decision variables
3. Constraints
4. Solutions that are Infeasible, Feasible and Optimal
5. Constraints that are Binding and Slack

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