Solving problems with systems of inequalities  TOPIC_SOLVED

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Solving problems with systems of inequalities

Postby onmyown on Tue Mar 08, 2011 9:09 pm

Hi, I am completely not getting how to solve this problem involving systems of inequalities.

Here is the question:
What is the maximum value of 2x+3y+4, subject to the constraints listed below?
x>0
y<0
x>5
y>-4


I know the answer to the question. And I know that in order to solve this question I need to check the corners of the feasible region. These are the points: (0,0), (5,0), (0,-4), and (5,-4). And, to substitute each of these ordered pairs into the expression 2x+3y+4.

I just don't understand how those points were determined. I tried graphing the inequalities, but I am still not getting those points. For instance, I don't understand how y< is the same as (5,0). Why is the x-value 5 in this ordered pair? As far as I understand there is no information given in the inequality to determine what the x-value would precisely be for an ordered pair.

can anyone please clarify some of this for me? How do I exactly get the ordered pairs?
Thank you very much
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Postby stapel_eliz on Tue Mar 08, 2011 10:58 pm

onmyown wrote:For instance, I don't understand how y< is the same as (5,0).

It isn't. Instead, try graphing the system of inequalities and finding the coordinates of the corner points. (Note: I suspect that your third inequality is actually "x < 5".)

Then plug those corner points into the optimization equation.

(For a complete explanation of the process, try here.) :wink:
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Re:

Postby onmyown on Wed Mar 09, 2011 2:00 am

stapel_eliz wrote:
onmyown wrote:For instance, I don't understand how y< is the same as (5,0).

It isn't. Instead, try graphing the system of inequalities and finding the coordinates of the corner points. (Note: I suspect that your third inequality is actually "x < 5".)

Then plug those corner points into the optimization equation.

(For a complete explanation of the process, try here.) :wink:


the link helped me a lot.

oh btw, you were right its actually x<5. I copied out the problem to fast :oops:

Thank you for the help!
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