Kate is considering investing in stocks. Her broker suggests ten different stocks, namely, 1, 2, 3, 4, 5, 6, 7,8,9 and 10 . She wants to formulate the stock selection problem subject to the following constraints. Using the binary variables xi ( 1 , if she invests in stock i;0, otherwise) for stock i, and additional variables if needed, formulate the following constraints. (a) (5 points) To lower the risk of losing money, she should invest in at least 4 stocks out of these 10 stocks. (b) (5 points) She can invest in stock 5 only if she invests in both stocks 6 and 7 . (c) (5 points) She has to invest in stock 5 if she invests in both stocks 6 and 7. (d) (5 points) She has to invest in stock 5 if she invests in stock 6 or 7. (e) (5 points) Her broker suggests the following two combinations: either choose at least two from stocks 1,2,3, and 4 , or at most three stocks 5,6,7,8 and 9 . (f) (5 points) Among stocks 5,6, and 7, Kate has to invest in either all of them or none