Simultaneous Inequalities

Hi Guys,

This one is long problem. I figured out most of it, but need a hint with the last proof part.

Draw a diagram illustrating the region S of the xy-plane which is defined by the simultaneous inequalities , and give the coordinates of the vertices of S. Prove that, if line intersects S, then .

The Point P lies on y = kx and is in the region S. Prove that, when , the maximum value for the y-coordinate of P is and find the corresponding expression when

I completed the initial parts of the problem. Got the 3 vertices of the region S,

Then since y = kx must pass through A or C, got max and min slopes and hence proved, .

I am stuck at the next part of the problem. Any ideas? Thanks for your help!