I am not sure whether I have done this right or that my answer is correct. I have a strong feeling that tells me it is not right. Could you please check it for me?

Minimize

C = x + y

subject to the constraints

1x +7y ≥ 1

11x + 2y ≥ 1

x, y ≥ 0

The answers I got through solving the system geometrically/graphically is that the minimum of C is 0.244360901 and occurs when x = 0.11842105 and y = 0.125939849.