In 2-variable linear programming problems, constraints can take the form of either $aX+bY < C$ or $mX > nY$. Both lines graph to form linear bounds so the graphical solution applies. But in 3+ variable problems, you need to use the Simplex method, and the calculators for the Simplex method apparently don't accept constraints of the form $mX > nY$.
I tried converting them algebraically to $mX-nY > 0$, but in a 2 variable problem the Simplex calculator gives me "no solution" when the graphical method finds a solution. Is there another way to enter these sorts of constraints in Simplex calculators?
This the problem I tried:
Maximize: $Z=5x+7y$
$x+y≤30$
$2x+y≤50$
$4x+3y≥60$
$2x≥y$
$x≥0,y≥0$
The graphical method finds that the solution is $x=10, y=20, Z=190$.
I entered that into the online calculator here as
$F(x)=5X1+7X2$
$1X1+1X2≤30$
$2X1+1X2≤50$
$4X1+3X2≤60$
$2X1+-1X2≥0$
And it returns:
"Answer:
The system has no solutions or has many solutions."
You changed $\ge 60$ to $\le 60$, and you also need to specify the $\ge 0$ bounds. But even with these changes, that online calculator yields the wrong conclusion. The online calculator provides the complete steps for the big-M method. After the first step you notice that it has a basis where $x_{10}=-30$, which is not feasible. Apparently it makes an error with the ratio test. The same website has a dual simplex solver which gives the correct output.
However, I verified your solution graphically here.