What type of programming is this problem?

Question

I have a program as follows:

$$ minimize \quad t \\ S.T.: \quad 3x_1+2x_2+x_3+2x_4 \le t \\ \quad x_1+x_2+5x_4 \le t \\ \quad x1+x_2+2x_3+3x_4 \le t $$

In this formulation, $t$ is the objective function, $x_1,\ x_2, \ x_3$ and $x_4$ are input variables. The program has linear (convex) combination of inputs as the left hand side of its constraints.

I want to know if it can be considered as linear program?

Can it be considered as convex or non-convex program? I know that if it is linear, it is convex.

Answer 1

This is considered a linear program (or linear optimization problem). This may be easier to see for you if you rename $t$ to $x_5$ and move it to the left hand side of each constraint.