Why a negative coefficient of variable means it is not optimal in simplex method?

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Why a negative coefficient of variable means it is not optimal in Simplex method?
Which means why we should make all coefficient non-negative(positive) for optimization of MAX linear programming problem?


When we have the following MAX problem.

MAX 3x + 5y

This can be transformed to the Standard form:
z - 3x - 5y

As long as we have a negative coefficient in this standard form equation then there is still a way to increase 'z' value by increasing 'x', 'y' as well. However, when having positive one :
z + 3x +5y

then there is no way to increase 'z' value unless 'x' or 'y' has a negative value. Which is not available by the condition:
S.T.
x, y >0


Therefore, in order to find the optimum solution of MAX problem, we only need to make sure all coefficients are positive of Objective Function equation.

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