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Minimize Z= x + 2y, subject to constrain...

Minimize Z= x + 2y, subject to constraints are ` 2x + y ge 3, x + 2y ge 6 , " and " x , y ge 0 `. Show that the minimum of Z occurs at more than two point .

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It can be seen that the value of Z at points A and B is same . If we take any other point such as (2,2) on line x + 2y = 6 , then Z = 6 . Thus, the minimum value of Z occurs of more then 2 points . Therefore, the value of Z is minimum at every point on the line, x + 2y = 6.
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