Can number of constraints be less than number of variables in Linear Programming?

Question

In standard form of LP we have $n$ variable and $m$ constraint. In simplex algorithm we set all non-basic variable to zero and at most $m$ basic variable have positive value.

if $m < n$, then at least $n-m$ variables would be zero. Is it a valid LP problem? Can solve a LP that $m < n$?

Answer 1

Minimize $f(x_1,x_2)=x_2$ where $x_1, x_2\geq 0$.

[In the sense of linear programming this would count as a problem with zero constrains. In standard form the non-negativity of the variables is always there, so one would rather count the constrains that are equations.]