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