Question 1088154
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Your case is very special: it is degenerated in some sense.


Your difficulties go from the fact that "the object function" z = 0.4x - 0.2 y is "parallel" to the line 2x - y = 5.


Therefore, all the points at this line create the same value of the objective function.



Did your teacher or your textbook  touched you on this subject ?


It is the degenerated case of the linear programming method.



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For the regular case of the linear programming method see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Solving-minimax-problems-by--the-Linear-Programming-method.lesson>Solving minimax problems by the Linear Programming method</A> 

in this site.