Question 29145
Minimize C = 2x + y with the following constraints:
-3x +4y< = 12
3x + 2y < = 6
y> = 0
LET US GRAPH THESE 3 GIVEN CONDITIONS....
-3x +4y = 12...................I
3x + 2y  = 6.................II
y = 0.......................II

{{{ graph( 600, 600, -10, 10, -10, 10, (12+3*x)/4, (6-3*x)/2,0) }}}

WE FIND THE VERTICES OF THE TRIANGLE FORMED BY 3 CONDITIONS...I,II AND III... AS (0,3),(-4,0) AND (2,0)
FIND THE VALUE OF GIVEN FUNCTION 
C= 2X+Y AT THESE 3 POINTS
WE GET 
C1=2*0+3=3
C2=2*-4+0=-8
C3=2*2+0=4
C2 =-8 IS MINIMUM...IF NEGATIVE ANSWERS ARE NOT ALLOWED FOR C ( THOUGH IT IS NOT MENTIONED IN THE PROBLEM) THEN C1=3 IS MINIMUM.