I am having trouble with the following problem.

"Mathematically characterize the set of objective coefficients (c1,c2) for which the following LP has a finite optimal solution.

MAX z= c1x1 + c2x2
x1 - 2x2 <= 8
x1 >= 2
2x1 + 3x2 >= 12
x1, x2 >= 0

Please Let me know if you can help.
Do we need to find the extreme directions...? and if so how...?
We know that we need to use a theorem... in our book it is THM3.5...