Authorized and available shares

Aspin Corporation's charter authorizes issuance of 2,000,000 shares of common stock. Currently, 1,400,000 shares are outstanding, and 100,000 shares are being held as treasury stock. The firm wishes to raise $48,000,000 for a plant expansion. Discussions with its investment bankers indicate that the sale of new common stock will net the firm $60 per share.

a. What is the maximum number of new shares of common stock that the firm can sell without receiving further authorization from shareholders?

b. Judging on the basis of the data given and your findings in part a, will the firm be able to raise the needed funds without receiving further authorization?

c. What must the firm do to obtain authorization to issue more than the number of shares found in part a?

Please provide your own work. Thanks.