You has a margin account with $$100,000$ and would like to trade AAPL stock. The initial margin requirement is $50\%$ and the maintenance margin is $30\%.$ The current market price of AAPL is $ $180.$

a$)$ You believe that AAPL is undervalued and would like to take a long position. Whats the maximum number of shares you can buy? What price can AAPL fall before you will receive a margin call?

b$)$ You believe that AAPL is overvalued and would like to take a short position. Whats the maximum number of shares you can sell short? What price can AAPL increase before you will receive a margin call?