## Linear Programming: Min 2A + 3B s.t. 1A+3B<=12, 3A+1B>=13, ...

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needhelp2
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### Linear Programming: Min 2A + 3B s.t. 1A+3B<=12, 3A+1B>=13, ...

I am stucktrying to solve for the following:
Min 2A + 2B
s.t.
A. 1A + 3B <= 12
B. 3A + 1B >= 13
C. 1A - 1B = 3

I need to
A. Show the Feasibility Region
B. What is the extreem point of the feasible region
C. Find the optimal solution using the graphical solution procedure.

I found my lines:
A.(0,4) (12,0)
B. (0,13)(4.333,0) This one I am unsure
C. (0,-3)(3,0)

I believe my extreme points of feasibility have to be on the line because of equation C, however dont know how to get to it.
I can add lines B and C (4,1)
but when I add lines A and C I get confused.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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I found my lines:
A.(0,4) (12,0)
B. (0,13)(4.333,0) This one I am unsure
C. (0,-3)(3,0)
What you have posted are pairs of points. Perhaps you mean that you have found points so that you can now draw the lines...?
I believe my extreme points of feasibility have to be on the line...
I'm not sure what you mean by the above...? As your book and instructor should have mentioned (and as the lesson provided to you in your previous thread explained), the points to test in the optimization equation are the corner points of the feasibility region. So you need to find the intersections of the various pairs of lines (or look on the graph, if the points are "neat" whole numbers).
dont know how to get to it.
I can add lines B and C (4,1)
but when I add lines A and C I get confused.
When putting two equations equal (for instance, B = -(1/3)A + 4 and B = -3A + 13/3), you are, in effect, solving a system of equations. To learn how that works, please try here.