Hi All
I used CVX to solve a simple feasibility check as follow

cvx_begin
variable ho
% maximize 0
subject to
hmin <= ho <= hmax
ho <= 110;
cvx_end

Since the constraints are affine I was expecting the value of ho to be min (hmax,110). But the solution
which I am getting is 59.8329. input values are hmax =300, hmin =10;

You get a feasible point, so all is fine. If you try different solvers you can even get different feasible points. What you describe later would require you to maximize ho.

I believe what you are thinking about is a solution given by the simplex algorithm, where indeed the solution is at a vertex. But if you use another algorithm, the solution is not nesseraily at a vertex. You obtained a correct solution so all is fine.