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
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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
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