$3\mathrm{.}4.$ For each of the following optimization problems, $($a$)$ show that it is convex, $($b$)$ write a

$($x$)($optimal value $0\mathrm{.}00246914)$

CVX$/$CVXPY code that solves it$,$ and $($c$)$ write down the optimal solution and optimal

value $($by running the CVX$/$CVXPY code$).$ Note: The optimal value of each problem

min,$(x_1+x_2+x_3{)}^8+x_1^2+x_2^2+3x_3^2+2x_1{x}_2+2x_2{x}_3+2x_1{x}_3$

$s.t.(|x_1-2x_2|+1{)}^4+\frac{1}{x_3}10,$

$2x_1+2x_2+x_{3}1,$