## Linear Program using graphical solution

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
needhelp2
Posts: 3
Joined: Tue Feb 22, 2011 3:43 am
Contact:

### Linear Program using graphical solution

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

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
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?

needhelp2
Posts: 3
Joined: Tue Feb 22, 2011 3:43 am
Contact:

### Re: Linear Program using graphical solution

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.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
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.
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.
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.
1B<= 80 is a horizontal line on the graph
Yes.
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.)
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.