Question

# Solve the following Linear Programming problems graphically:1. Maximize $$Z = 3x + 4y$$       Subject to the constraints : $$x + y \le 4, \, x \ge 0 , \, y \ge 0$$2. Minimize $$Z = -3x + 4 y$$       subject to $$x + 2y \le 8 , \, 3x + 2y \le 12, \, x \ge 0 , \, y \ge 0$$

Solution

## 1.       Maximize $$Z=3x+4y$$     Corner points Value of $$Z=3x+4y$$   (0,4) 16 (4,0) 9 (0,0) 0   Hence, Z is maximum at $$(0,4)$$ and max value is $$16$$     2.       Minimize $$Z=-3x+4y$$ Corner points Value of $$Z=-3x+4y$$ (0,4) 16 (2,3) 6 (4,0) -12   Hence, Z is minimum at $$(4,0)$$ and min value is $$-12$$Mathematics

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