Maximize $z=5x_1+3x_2$ subject to the following constraints:$x_1+x_2\ge 3$$x_1-x_2\le 2$ and the solution is in the first quadrant ($x_1,x_2\ge 0$). What can be said about the solution of this LPP?

Let's analyze the feasible region:$x_1+x_2\ge 3$ represents the area above or on the line passing through $(3,0)$ and $(0,3)$.$x_1-x_2\le 2$ represents the area above or on the line passing through $(2,0)$ and $(0,-2)$.$x_1,x_2\ge 0$ restricts the region to the first quadrant.The intersection of these half-planes forms a region that extends infinitely in the positive $x_1$ and $x_2$ directions. Since we are maximizing $z=5x_1+3x_2$ and the region is not enclosed (unbounded) in the direction of increasing $x_1$ and $x_2$, the objective function can increase indefinitely.Therefore, the LPP has an unbounded solution.