The top 5 stocks in the S&P 500 index, when ranked by market capitalization, make up 22% of the total market capitalization of the S&P 500 index. Numerical estimates of the mean (or expected) rates of return values of these top five stocks, expressed in decimal (not percentage) form, are listed in the table below. STOCK AAPL Apple, Inc. Amazon.com Inc. Microsoft Corp. Alphabet, Inc. Facebook, Inc. TICKER AAPL 0.21 AAPL AMZN 0.12 AMZN MSFT GOOG FB MEAN RETURN MSFT 0.17 0.69 0.65 The variance of returns (entries on the main diagonal) and covariances between returns of these top five stocks, expressed in decimal (not percentage) form, are as follows: 0.44 0.36 0.41 GOOG 0.13 FB 0.16 AMZN MSFT GOOG FB 0.12 0.17 0.13 0.16 0.15 0.12 0.10 0.12 0.12 0.19 0.14 0.15 0.10 0.14 0.15 0.14 0.12 0.15 0.14 0.21 Assuming there is a risk-free asset available in addition to these 5 risky assets, determine the portfolio weightings for each of these stocks of the unique fund F as defined in the One-fund theorem of Modern Portfolio Theory. Note that short positions (negative weights) are permissible and the sum of all the weights must be equal to one. The annual risk-free rate is 5%. What is the optimal portfolio weight for Amazon.com Inc. (ticker: AMZN)? Please express your answer in decimal (not percentage) form and round your numerical answer to two decimal places. You would like to invest $10,000 and seek an expected return of 75% annually. A friend tells you that this is impossible since the stock with the highest annual expected return, from the table above, is AAPL with an expected annual return of 69%. Your friend advises you to invest all the $10,000 in AAPL. Assuming there is no risk-free asset available and short selling is allowed, is it possible to allocate your $10,000 amongst the 5 stocks in the table to achieve an expected return of 75%? If so, what is the optimal number of dollars to invest in AAPL such that the expected portfolio return is 75% while minimizing the portfolio variance? If not, then enter an answer of 10,000. Please round your numerical answer to the nearest integer number of dollars.