$3.(27$ points$)$ Let the production function of a firm be given by X$=$f$($l$,$k$)=3$l$^1/3*$k$^1/3.$ Let the cost of labor and capital be w$=$r$=2.$ Let the price of the produced good be shown by p$.$

$($a$)$ Find the conditional factor demands and cost function by solving the cost minimization problem.

$($b$)$ If p $=20,$ find the production level at which the firm maximizes its profit, the amount of labor and capital it will use, its total cost and its profit.

$($c$)$ Obtain the same result by solving the firm's profit maximization problem.