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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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