Options
(A) (9,0) (B) (-2,20) (C) (-5,2) (D) (0,-9)
Answer:
(B) (-2,20)
Explanation:
Given the objective function, C=3x-4y
The vertex at which C is minimized will be the point (x,y) at which the expression gives the lowest value.
Option A
At (9,0), x=9, y=0
C=3(9)-4(0)=27-0
C=27
Option B
At (-2,20), x=-2, y=20
C=3(-2)-4(20)=-6-80
C=-86
Option C
At (-5,2), x=-5, y=2
C=3(-5)-4(2)=-15-8
C=-23
Option D
At (0,-9), x=0, y=-9
C=3(0)-4(-9)=0+36
C=36
The lowest value of C is -86. This occurs at the vertex (-2,20).
Therefore, the objective function C=3x-4y is minimized at (-2,20).