If a hedge fund has 1 million dollars in account. The current price of stock A is 100 dollars per share and the price of stock B is 80 dollars per share. Assume the two portfolios have no dividend payment. Now the fund decides to take the following strategy: buy stock A and short stock B. For two share of stock A bought, one share of stock B will be shorted. Assume that borrowing rate is 0, the initial margin requirement for both margin trading and short sale is 50%.

1. (a) (8 points) If the fund want to buy 200 shares of stock A and she finances 50% of this investment using borrowing. Write out the balance sheet.

2. (b) (8 points) If the fund want to buy 200 shares of stock A, how many shares of B will be shorted? Write out the balance sheet.

3. (c) (6 points) With the capital of 1 million dollars, how many shares can the fund buy stock A at most following the strategy (buy 2 shares of A short 1 share of B)?