1. you can trade in the 30-year Treasury Bond Future contracts market. The initial margin requirement is 10% of the underlying asset face value, and the maintenance margin is 5% of the underlying asset face value. For simplicity, assume that the price limit rule of the future exchange is such that the maximum daily margin account change is 3% of the underlying asset face value. Now you have the authority to invest 100 billion dollars, and the internal trading desk liquidity quota is 8 billion dollars (that is to say, each day you can ask for at most additional 8 billion dollars from the firm given a margin call from the exchange). To guarantee that you will stay with your position as long as you want, what is the maximum amount of contract you can take and what is your position (long or short)?