Passing Marks

Recently, Chef's College Examination has concluded. He was enrolled in $3$ courses and he scored $A, B, C$ in them, respectively. To pass the semester, he must score at least $A_{min}, B_{min}, C_{min}$ marks in the respective subjects along with a cumulative score of at least $T_{min}$, i.e, $A + B + C \ge T_{min}$. Given seven integers $A_{min}, B_{min}, C_{min}, T_{min}, A, B, C$, tell wheth