Question

linear programming problem is to maximize Z= 4x - 3y subjected to constraints x>= 0, y>=0, x+2y<= 4, 3x-2y<=6 then the objective function is
(A) 3x-4y (B) 4x-3y (C) Not defined (D) x=y

Answer 1

Answer:

The answer is b.) 4x - 3y

Step-by-step explanation:

Linear programming problem to maximize Z  = 4x - 3y

The given constraints are

i) x ≥ 0

ii) y ≥ 0

iii) x + 2y ≤ 4

iv) 3x - 2y ≤ 6

First we graph the constraints and find the intersection or vertex points.

The vertex points are (0,0), (2,0), (0,2) and (2.5, 0.75)

The value of Z for (0,0) is Z  = (4×0) - (3×0) = 0

The value of Z at (2,0) is Z  = (4×2) - (3×0) = 8

The value of Z at (0,2) is Z =  (4×0) - (3×2) = -6

The value for Z at (2.5, 0.75) = (4×2.5) - (3×0.75) = 7.75

The maximum value for Z = 4x - 3y is found at the vertex (2,0)

The objective function is b.) 4x - 3y