Sensitivity analysis in linear programming Could someone please explain in detailed steps how to apply a sensitivity analysis to such problem:
$$maximize \ \ 2x_1 + 3x_2 \\
s.t. \ \ 4x_1+3x_2≤600 \\ 2x_1+2x_2≤320 \\ 3x_1+7x_2≤840 \\ x_i≥0$$
The goal is it to determine the boundaries of $x_2$.

I am not particularly keen to do your homework for you "in detail". But here is a starting point. The red line is a contour of $2x+3y$. The blue line is $4x+3y=600$; the orange line is $x+y=160$; the green line is $3x+7y=840$. The other lines are $x\ge0,y\ge0$.
The first question to settle is obviously where the allowed area is. It is in fact the area "below" the green, orange and blue lines but in the first quadrant. So the allowed area is the irregular pentagonal area shown in the plot.
Ignoring sensitivities we would maximise $2x+3y$ at the intersection of the green and orange lines, because we want the red line to be as far "upwards" as possible (whilst keeping its slope fixed).
You say nothing in the question about what kind of sensitivity analysis you want. There are a whole range of things you can change. You can "change the RHS", meaning that you shift the constraint lines, whilst keeping their slopes unchanged. Here you can see that the blue line is a "non-binding" constraint - shifting it will not change the optimisation for unless you shift it further to the left than the intersection of the green and orange lines. On the other hand, the green and orange constraints are "binding" - any shift however small will shift the optimisation.
Another sensitivity is to "change the objective function coefficients". In other words you change the coefficients 2, 3 in $2x+3y$. That has the effect of changing the slope of the red line and hence the optimisation.
Finally, of course, you can change the coefficients in the constraints, thus changing the slopes of the blue, green, orange lines. Again small changes to the blue line will make no difference, but small changes to the orange and green lines will.

