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

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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.