Find the maximum value of 4x+y (system of inequations)

The max will occur at a "corner point" but this is very hard to identify with a graph because there are so many "overlapping"  graphs....

WolframAlpha gives the following solution : 

https://www.wolframalpha.com/input/?i=maximize+4x+%2By+given+3x%2By++%E2%89%A4+31+,++2x%2By++%E2%89%A4+23,+++2x-y++%E2%89%A4+14,+++x%2B6y++%E2%89%A5+20,+++y+%E2%89%A4+11,+++y+%E2%89%A5+0,+++x+%E2%89%A5+2

It appears that the max occurs at (9, 4)   and the max is  4(9)  + 4   = 40

Here's the Desmos graph : https://www.desmos.com/calculator/opl1cuchfu

Maybe you can find the max corner point much easier than I can.......!!!!!

Let's look at this again......and we will remove the last 3 constraints.....these three just tell us that  the solution will occur in the first quadrant  where x  ≥ 2  and   y ≤ 11

Look at the graph now : https://www.desmos.com/calculator/upxf7i7tbd

If I read the graph correctly.....[a real leap of faith]...there appear to be only two corner points that satisfy the constraints....they are

(8,2)   and (9,4).......but only one will maximize  4x + y....and that occurs at (9,4)