How to minimize this equation

I need some help with hw. please tell me how to minimize C=2x+y with the following constraints:
-3x+4y 3x+2y y>or=0

Thanks! Please tell me how to do it too

Boundaries of enclosed area are

-3x + 4y = 12
3x + 2y = 6
y = 0

graphic of boundaries: http://www.wolframalpha.com/input/?i=-3x…

corners of enclosed area are where

-3x + 4y = 12
3x + 2y = 6
(x , y) = (0 , 3) <== first test point

-3x + 4y = 12
y = 0
(x , y) = (-4 , 0) <== second test point

3x + 2y = 6
y = 0
(x , y) = (2 , 0) <== third test point

C = 2x + y

2 * 0 + 3 = 3 <== first test values
2 * (- 4) + 0 = - 8 <== second test values
2 * 2 + 0 = 4 <== third test values

x = - 4 ; y = 0 <=== produces the minimum value for C