https://www.desmos.com/calculator/3e75rstepl

Find the maximum value of x+y in the polygon.

Introduce a new equation

x+y=c

let c be a slider.

now slide ist and see where the biggest value of c is.

I got the approx value of 2.72 but you can get the exact values from the equation.

https://www.desmos.com/calculator/xs7alxvmny