When the value indicated by the circle is a valid value for the inequality.
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I dunno an who cares! we use closed circles when we include the number on which it is and if we dont want to include it then we use open circle
strict inequality
An open or closed circle are used to graph an inequality in one variable. An open circle is used if the value at the end point is excluded from the feasible region while a closed circle is used if the value at that point is within the accepted region.
Linear programming is just graphing a bunch of linear inequalities. Remember that when you graph inequalities, you need to shade the "good" region - pick a point that is not on the line, put it in the inequality, and the it the point makes the inequality true (like 0
The part that is shaded represents all the possible solutions. An inequality has solutions that are either left or righ, above or below or between two parts of a graph.