Consider the following multi$-$objective constrained optimization problem with three

design variables and two objective functions $f_1$ and $f_2$ :

minimize $f_1(x)=10x_1^2+5x_2^2-10x_3^2+90$

minimize $f_2(x)=5x_1{x}_3-5x_1{x}_2+20$

subject $to{g}_1(x)=3x_1^2+x_2^2-50$

$,h_1(x)=4x_1^2+3x_2^2+2x_3^2-17=0$

$($a$)$ Using weights $w_1=0\mathrm{.}2$ and $w_2=0\mathrm{.}8$ for the objectives $f_1(x)$ and $f_2(x)$ respectively,

write down the composite objective function $f(x)$ that should be minimized based on

the weighted sum of objectives approach.