Consider
$1\rightarrow{}x+2y\leq{500}$,
$2\rightarrow{}2x +y \leq{520}$,
$3\rightarrow{}2x+5y \leq{}1200$,
$4\rightarrow{}x \geq{}0$,
$5\rightarrow{}y \geq{}0$,
The above is the set of inequalities that generates a linear programming problem whose objective function is
$f(x,y)=9x +12y$,
I need to maximize the objective function, but the graphics are unclear when it comes to the points,
a) The problem to be solved is to produce a plot with enough detail with the coordinates of the solution polygon, drawn it by hand, with geogebra, symbolab and it is not possible to appreciate it well
b) I have never solved a linear programming problem with Mathematica and I would like to know how it can be done using mathematical syntax.
If you can help me, I would appreciate it very much
Notes
I do not know the symplex method.
This is not homework or a work assignment, it is for personal knowledge.
Update
error corrected