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

[ashina14]

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?

 

[Ray Vickson]

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