Graph the four inequalities. (I'm assuming you know how to do this.) It may help to change them into slope-intercept form, if you can:Given the constraints
x+y is less than or equal to 9
3x-y is greater than or equal to 0
x is greater than or equal to 0
y is greater than or equal to 0
You'll find that the intersection of these graphs (all of these graphs are solid lines where one area that each line divides gets shaded) will be a triangle. The vertices of the intersecting area are your critical points that you will need to test into the function
In our case, there are three critical points. Two of them are easy to find. The other is a point that is an intersection of two lines. Plug in these points into f(x). The smallest value of f(x) is your minimum.