Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
4. Linear Programming
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Exercise 19 Page 161

Graph the given system and determine the vertices of the overlapping region. Substituting these vertices into the equation will help you find the maximum value.

Graph:

Vertices:
Maximum: at

Practice makes perfect
Our first step in finding the maximum value of the given equation is to graph the given system and determine the vertices of the overlapping region. Substituting these vertices into the equation, we will find the maximum value.

Inequality I

To write the equation of the boundary line for the first inequality, we will change the inequality symbol to an equals sign.
Let's rewrite this equation in slope-intercept form.
Now we can determine its slope and intercept to draw the line.
Now that we know the slope and intercept, let's use these to draw the boundary line. Notice that the inequality is non-strict, which means that the line will be solid.
To complete the graph, we will test a point that is not on the line and decide which region we should shade. Let's test the point If the point satisfies the inequality, we will shade the region that contains the point. Otherwise, we will shade the other region.