Expert: andy vong - 8/29/2007

Question
QUESTION: I am having a lot of trouble understanding one of my problems in my textbook. I just cannot seem to get the correct answer and how to obtain the correct answer. The problem is: Find the coordinates of the vertices of the figure formed by the system of inequalities: x>-1,y>-2, and 2x+y<6. Can you please explain to me how to do these kind of problems. Thank you for your time.


ANSWER: Hi kristine,

Sorry for the delay I'm still having problems with my PC.  

Begin by graphing each inequalities.  The 3 lines will enclose a figure find the vertices of that figure.  The vertices represent where 2 lines intersect each other.

The first inequality x>-1 is a vertical dashed line passing through x=-1[note: a dashed line is used to show that the left side can not equal the right side; a solid line is used to show that the left side can equal the right side].  Shade region to the right since x>-1.  The second inequality y>-2 is a horizontal dashed line passing through y=-2.  Shade region above the line since y>-2.  Finally the third inequality is an oblique dashed line where its x-int. is at (3,0) and y-int at (0,6).  Shade the region below the line since all the points make 2x+y<6 true.[note:  use (0,0) as the test point].  Find where all 3 shaded regions overlap and look for the vertices of the figure form by all 3 lines.  Any method[elimination, substitution, graphing] can be used to find the vertices.

Hope this helps

---------- FOLLOW-UP ----------

QUESTION: I have another question for you... can you explain to me how to find the maximum and minimum value f(x,y)=x-4y for the feasible region... this is another problem that I have been having a lot of trouble with and no one has been able to help me any.. thank you if you are able to help me once again.
ANSWER: Hi kristine,

The maximum and minimum are produced from the corner points of your feasible region.  Another word for corner points is vertices.  Find your vertices or corner points using one of the methods for solving systems of equations(elimination, substitution, graphing).  Plug in the vertices into the function the highest number represents the maximum the lowest number represents the minimum.  

Hope this helps

---------- FOLLOW-UP ----------

QUESTION: the only problem I am having now is: this is the only set of numbers that I have: f(x,y)=x-4y....
what do I do? please help....
ANSWER: Hi Kristine,

I'm confused with question.  Which set of numbers are you referring to?  If you have the corner points substitute them into the f(x,y).  The highest is the max and the lowest number is the min

Hope this answers your question.

---------- FOLLOW-UP ----------

QUESTION: can you help me fully understand how to get the corner points that I need to plug them in the equation? then can you help me on solving the problem to get the max and min number. thank you... sorry, I am doing my courses at home and I don't have someone there to explain this to me fully to where I understand what to do. thank you again...you have been a big help.

Answer
Hi kristine,


It is very difficult to explain without a graph.  I'm assuming that you have no problems graphing and locating the feasible region.  I explained how to do this earlier.  You would use one of the methods in solving systems of equations to find the point of intersection.  Be sure you can tell which lines intersect each other.  

Hope this helps