
To find: the coordinates of all the vertices and determine whether the solution set bounds or not.

Answer to Problem 26E
The vertices are
The solution set is bounded
Explanation of Solution
Given:
Calculation:
We obtain the equations of the straight lines from the given inequalities as
Solving these two equations we get the intersection point of the straight lines.
Multiply second equation by -2 and then add with the first equation.
Substitute
So, the intersection point is (3,2)
The intercept form of the first straight line is
So, this line intersect
The intercept form of the second straight line is
So, this line intersect
We graph the lines given by the equations that correspond to each inequality. To determine the graphs of the linear inequalities, we need to check our test point. Here, we take (0,0) as test point.
Inequality | Test point (0,0) | Conclusion |
Satisfied inequality | ||
Satisfied inequality |
Since (0,0) is below the lines $4 x+3 y=18$ and $x+2 y=8$, our check shows that the region on or below the lines must satisfy the inequalities. The inequalities
Therefore, graph with shaded region is
Vertices:- The co-ordinate of one vertex is the point of intersection of the given lines, which is clearly (3,2) . The origin (0,0) is also a vertex. The other two vertices are at the
Therefore, the vertices are
From the figure it is clear that the shaded region is bounded. Therefore, the solution set is bounded
Conclusion:
Therefore, the vertices are
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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