c$.(10$ points$)$ Consider the optimization problem below, where b and $a_4\text{'}$s are provided as param: eters:

max $\{$:$ma{x}_{s.t.}{\displaystyle \underset{i=1}{\overset{2}{}}}{a}_1,x_2\}$

Lincarize the maximum value between $x_1$ and $x_2$ using additional variables and constraints. Prowide the modifications nereskary for the criginal model.