On March$08,2019,$ Lightspeed POS$$ Inc., a$$ Montreal$-$based company that provides retailers and restaurants with$$ cloud$-$based software to help them manage$$ point$-$of$-$sale and$$ back$-$office functions, conducted its initial public offering$($IPO$)$ of common stock. In the primary trading$$ market, the$$ company's shares were priced at $$$$29\mathrm{.}8429\mathrm{.}84$ per$$ share, but after one day of trading on$$ TSX$,$ the share price closed at $$$$38\mathrm{.}1738\mathrm{.}17.$ The company sold $22\mathrm{.}122\mathrm{.}1$ million shares in the offering.

a$.$ To what extent$($in dollars and on a percentage$$ basis$)$ was$$ Lightspeed's stock underpriced in its$$ IPO?

b$.$ How much cash$($before deducting fees to investment$$ banks$)$ did Lightspeed$$ raise? How much more would it have raised if the shares had not been$$ underpriced?