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If Y=MAX((3x+y),(11x-y)) Then What's The Value Of Y?

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Oddman answered
Under the conditions that the maximum of the expression is 3x+y, we have
   3x + y > 11x - y
   2y > 8x
   y > 4x
and
   y = 3x + y
   0 = 3x
   x = 0
For x=0, y can be any positive number.
Under the conditions that the maximum of the expression is 11x-y, we have
   3x + y < 11x -y
   y < 4x
and
   y = 11x - y
   2y = 11x
   y = 5.5x
or
   5.5x < 4x
   1.5x < 0
   x < 0
For x < 0, y = 5.5x
A graph of this equation will be a (half) line of slope 5.5 to the left of x=0, and a (half) line x=0 above the x-axis.


There is no solution for x > 0.

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