Linear Program using graphical solution  TOPIC_SOLVED

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Linear Program using graphical solution

Postby needhelp2 on Tue Feb 22, 2011 3:57 am

I am trying to solve the following linear program using the graphical solution procedure:
Max 5A + 5B
s.t.
1A < or = 100
1B < or = 80
2A + 4B < or = 400
A,B >or = 0
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Postby stapel_eliz on Tue Feb 22, 2011 12:00 pm

needhelp2 wrote:I am trying to solve the following linear program using the graphical solution procedure...

Okay. How far have you gotten?

You started with assigning each variable to an axis (say, the A variable to the x-axis and the B variable to the y-axis), graphed the system of linear inequalities, solved pairs of equations to find the corners of the feasibility region, and... then what? Where did you get stuck in the linear-programming process?

Please be complete. Thank you! :wink:
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Re: Linear Program using graphical solution

Postby needhelp2 on Thu Feb 24, 2011 6:12 am

Yes I need to graph and solve the equation.
Max 5A + 5B
s.t.
1A < or = 100
1B < or = 80
2A + 4B < or = 400
A,B >or = 0

1A<= 100 is a vertical line on the graph (I think it is vertical, but I am not sure. My reasoning is A is on the X axis)

another question about my graph; starting from the Orgin if "0" do I start my numbers at 100, 200, 300 ... or since the distance is so close should I do in increments of 10s --- 10,20, 30 Is there a rule of thumb for this?

1B<= 80 is a horizontal line on the graph

2A + 4B <= 400 here is where I am stuck.

to solve I substitue "0" for both A and B each time and I get the following points

(200,0)
(0,100)
I plot both of these points. My extreme points are (100,50) and (40,80)

where do I go from here, not sure what this means as it relates to 5A + 5B.
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  TOPIC_SOLVED

Postby stapel_eliz on Thu Feb 24, 2011 12:19 pm

needhelp2 wrote:Yes I need to graph and solve the equation.

To learn how to graph the solutions to systems of linear inequalities, please study this lesson.

needhelp2 wrote:1A<= 100 is a vertical line on the graph (I think it is vertical, but I am not sure. My reasoning is A is on the X axis)

Yes.

needhelp2 wrote:another question about my graph; starting from the Orgin if "0" do I start my numbers at 100, 200, 300 ... or since the distance is so close should I do in increments of 10s --- 10,20, 30

I think the above refers to the numbering on the axes. If so, then use whatever units you find useful and helpful.

needhelp2 wrote:1B<= 80 is a horizontal line on the graph

Yes.

needhelp2 wrote:2A + 4B <= 400 here is where I am stuck.

Solve the inequality for whichever variable you've put on the y-axis. (To learn how to solve linear equations for "y", try here.) Then graph as usual (shown in the first lesson link, above.)

needhelp2 wrote:My extreme points are (100,50) and (40,80) where do I go from here, not sure what this means as it relates to 5A + 5B.

Then you plug the extreme points into the optimization equation, and see which one is the best fit to the requirements of the exercise. For worked examples, please review this lesson. :wink:
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