I have to graph two linear systems and solve them geometrically. However, I am finding that one linear equation in the system contradicts another. Please note that those are two linear systems I have set up myself in the process of solving a 2x2 matrix game, so I'm not sure whether the linear systems I have arrived to themselves are right.
System 1
Objective function
F = x + y = 1/v
Constraints
x, y ≥ 0
1x + 7y ≥ 1
11x + 2y ≥ 1
Now, I first have to draw the boundaries of the constraints on the graph. I find some points of the boundaries and plot it. The boundaries are 1x + 7y = 1 and 11x + 2y = 1.
If x = 2 ("2" is greater than zero)
then 1(2) + 7y = 1, then y = -1/7
and 11(2) + 2y = 1, then y = -10.5
The results I get for "y" on the boundary are systematically negative, while the constraint x, y ≥ 0 require that both x and y are 0 or positive. I am confused. Is there something wrong with the linear systems themselves?