Suppose you are the lead underwriter for a start$-$up company. The company plans to sell $10$ million shares at the price of $$46$ per share. It also provides you an over$-$allotment option of $1\mathrm{.}5$ million additional shares. Recent road show estimates demand to be around $20$ million shares at $$46.$ There is lots of uncertainty about how the stock will perform after trading starts. Consider the following decisions. $18.$ Before the trading starts tomorrow, you need to allocate $($sell$)$ a number of shares to the institutional investors now at the IPO price. How many shares will you allocate? a$.9$ million shares b$.10$ million shares c$.11\mathrm{.}5$ million shares d$.15$ million shares e$.20$ million shares