Verify whether the following points are optimal solutions to the LP?

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The discussion centers on solving a linear programming (LP) problem with the objective to minimize the function 3x1 + 6x2 subject to the constraint 6x1 - 3x2 = 12 and non-negativity conditions x1, x2 >= 0. The user initially attempted a graphical solution but misunderstood the nature of the feasible region, which is unbounded rather than fixed. The conclusion is that there is a unique minimizing point for the given LP problem, confirming that the points (4,4) and (2,0) are not both optimal solutions.

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Homework Statement



Points (4,4) and (2,0)

Minimise 3x1+6x2
s.t. 6x1-3x2=12
x1,x2>=0



Homework Equations





The Attempt at a Solution



I tried solving this the way LP questions are solved in general, graphically.
So I drew a graph plotting the objective and the constraint but turns out there aren't enough constrains to have a fixed feasible region?! Either I move the objective along points on the constraint line only. Or there is something completely different required to do here?
 
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ashina14 said:

Homework Statement



Points (4,4) and (2,0)

Minimise 3x1+6x2
s.t. 6x1-3x2=12
x1,x2>=0



Homework Equations





The Attempt at a Solution



I tried solving this the way LP questions are solved in general, graphically.
So I drew a graph plotting the objective and the constraint but turns out there aren't enough constrains to have a fixed feasible region?! Either I move the objective along points on the constraint line only. Or there is something completely different required to do here?

This is wrong. You DO have a feasible region (I do not know what you mean by a "fixed" feasible region). The feasible region in this case happens to be unbounded (that is, contains points (x1,x2) where both x1 and x2 go to +∞) but that does not matter. In this case there is a unique minimizing point (so there are not two optimal points, just one).

RGV
 

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