An investment bank agrees to underwrite an issue of $15$ million shares of stock for Looney Landscaping Corp.

a$.$ The investment bank underwrites the stock on a firm commitment basis, and agrees to pay $$12\mathrm{.}50$ per share to Looney Landscaping Corp. for the $15$ million shares of stock. The Investment bank then sells those shares to the public for $$13\mathrm{.}25$ per share. How much money does Looney Landscaping Corp. receive? What is the profit to the investment bank? If the investment bank can sell the shares for only $$11\mathrm{.}95,$ how much money does Looney Landscaping Corp. receive? What is the profit to the investment bank?

b$.$ Suppose, instead, that the investment bank agrees to underwrite the $15$ million shares on a best effort basis. The investment bank is able to sell $13\mathrm{.}6$ million shares for $$12\mathrm{.}50$ per share, and it charges Looney Landscaping Corp. $$0\mathrm{.}275$ per share sold. How much money does Looney Landscaping Corp. receive? What is the profit to the investment bank? If the investment bank can sell the shares for only $$11\mathrm{.}95,$ how much money does Looney Landscaping Corp. receive? What is the profit to the investment bank?