Find the linear constraints for which the shaded area in the figure given is the solution set.
Consider A:
Given line x - y = 1
⇒y = x - 1
As the region given in the figure is above the y - intercept’s coordinates (0, - 1),
⇒y ≥ x - 1
⇒x - y≤1
Consider B:
Given line 2x + y = 2
⇒y = 2 - 2x
As the region given in the figure is above the y - intercept’s coordinates (0,2),
⇒y ≥ 2 - 2x
⇒2x + y ≥ 2
Consider C:
Given line x + 2y = 8
⇒2y = 8 - x
⇒y = 4 -
As the region given in the figure is below the y - intercept’s coordinates (0,4),
⇒y≤4 -
⇒2y≤8 - x
⇒x + 2y≤8
Consider D:
It is the region right side of the Y - axis.
It is x ≥ 0.
All the results derived:
x - y≤1
2x + y ≥ 2
x + 2y≤8
x ≥ 0