$1.$ Lauren has a margin account and deposits $$50,000.$ Assume the prevailing margin requirement is $40\%,$ commissions are ignored, and the GW company is selling at $$55$ per share. Margin transactions.

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a$.$ How many shares can Lauren purchase using the maximum allowable margin?

b$.$ What is Lauren$$s $ profit $($loss$)$ if the price of GW

c$.$ If the maintenance margin is $30\%,$ to what price can GW fall before Lauren will receive a margin call?