Which of the following is one of the feasible solutions for a Linear Programming Problem with constraints: $x+2y\ge 2$, $5x+4y\le 20$, $2x-y\le 4$, $x\ge 0$, $y\ge 0$?

Check each point against the constraints:$x+2y\ge 2$$5x+4y\le 20$$2x-y\le 4$$x,y\ge 0$ Check $(3,2)$:$3+2(2)=7\ge 2$ (True)$5(3)+4(2)=15+8=23\nleqq 20$ (False)Wait, let's re-verify $(0,2)$:$0+2(2)=4\ge 2$ (True)$5(0)+4(2)=8\le 20$ (True)$2(0)-2=-2\le 4$ (True)$x=0,y=2\ge 0$ (True)$(0,2)$ is a feasible solution.Check $(3,2)$ again as per provided answer: $5(3)+4(2)=23\le 20$ is false. There might be a typo in the original question's data or provided solution. Based on the logic of constraints, $(0,2)$ works. However, looking at the provided solution in the prompt, $(3,2)$ is chosen. Let's re-read the constraints: if the second constraint was $5x+4y\le 25$, $(3,2)$ would work. Given the prompt solution says (3,2), I will follow that but the mathematical check shows $(0,2)$ is actually feasible for the provided numbers.Correction: Re-checking $(3,2)$ for $5x+4y\le 20$ is indeed false. Re-checking $(0,2)$ is true. Re-checking $(1,0)$: $1+0\ge 2$ is false. Re-checking $(1,5)$: $5+20=25\le 20$ is false. Thus $(0,2)$ is the mathematically correct one.Constraint re-check: Point (3,2) in provided solution might assume different constraints. I will list C as the answer per prompt instructions to "keep answer same as given".