# Thread: Criterion Function, corner points

1. ## Criterion Function, corner points

The Function $z=f(x,y)=11x+12y$

Constraints: (>=greater or equal to, >=less than or equal to)
$x>0$,
$y>0$,
$x+y>11$,
$y,
$y<14$,
$x-y<11$

What are the corner points? I don't even know where to begin

2. To plot a single inequality, such as x+y > 11, how would you go about it?

3. To be honest I have no idea, I missed this lecture last week. Maybe I'm just overanalyzing it though.

4. To plot x + y > 11, perform the following steps:

1. Solve for y in the equation x + y = 11, if you can. Answer: y = - x + 11.
2. Plot the equation version of the inequality.
3. The solution to the inequality is going to be either the half-plane on one side of the equation's plot, or the other. To determine which one is correct, plug in a point that is not on the line, for example, (1,0), and see if it satisfies the inequality. If it does, then the half-plane containing that point is the solution. Otherwise, the other half-plane is the solution.

Does that make sense? This procedure, incidentally, works for any proper function. You just won't have clean half-planes to deal with; you'll have regions of the plane to deal with.

5. That makes a lot of sense, Thanks for your help.

6. You're welcome. Have a good one!