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.
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.