At which vertex is the objective function C=3x-4y minimized

Options

(A) (9,0) (B) (-2,20) (C) (-5,2) (D) (0,-9)

(B) (-2,20)

Step-by-step 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).

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints