$13\mathrm{.}3-4.$ Consider the following geometric programming problem:

Minimize $f(x)=2x_1^{-2}{x}_2^{-1}+x_2^{-2},$

subject to

$4x_1,x_2+x_1^2{x}_2^{2}12$

and

$x_{1}0,x_{2}0.$

$($a$)$ Transform this problem to an equivalent convex programming problem.

$($b$)$ Use the test given in Appendix $2$ to verify that the model formulated in part $(a)$ is indeed a convex programming problem.

$13\mathrm{.}3-5.$ Consider the following linear fractional programming problem:

Maximize $,f(x)=\frac{10x_1+20x_2+10}{3x_1+4x_2+20},$

subject to

$x_1+3x_{2}50$

$3x_1+2x_{2}80$

and

$x_{1}0,x_{2}0.$

$($a$)$ Transform this problem to an equivalent linear programming problem.

C $($b$)$ Use the computer to solve the model formulated in part $($a$).$ What is the resulting optimal solution for the original problem?

Please solve this questions below without ai and step by step.