The corner points for the feasible region determined by the system of linear inequalities
x + 4y ≥ 30
3x- + y ≥ 24
x,y ≥ 0
are A = (0,24), B = (6,6), and D = (30,0). If C = ax + by and a, b >0, determine conditions on a and b that will ensure that the minimum value of C occurs
(A) only at A
(B) only at B
(C) only at D
(D) at both A and B
(E) at both B and D