$a_{1,1}x_1 + a_{1,2}x_2 + \dots + a_{1,20}x_{20}\leq b _1$
$a_{2,1}x_1 + a_{2,2}x_2 + \dots + a_{2,20}x_{20} \leq b_2$
$x_1 \geq 0, x_2 \geq 0, \dots, x_{20} \geq 0$
$f(x) = a_{3,1}x_1 + a_{3,2}x_2+ \dots + a_{3,20}x_{20} $
All $a$'s and $b$'s are known. There are infinite solutions. I want to find values for $x$'s that solve the linear equations that maximizes $f(x)$. Not sure how to go about this. Not sure if my title is a very good way to summarize the question.