Suppose there is a relation r(A, B, C), with a B+-tree index with search key (A, B).

a. What is the worst-case cost of finding records satisfying 10 < A < 50 using this index, in terms of the number of records retrieved n₁ and the height h of the tree?

b. What is the worst-case cost of finding records satisfying 10 < A < 50 ∧ 5 < B < 10 using this index, in terms of the number of records n₂ that satisfy this selection, as well as n1 and h defined above?

c. Under what conditions on n1 and n2 would the index be an efficient way of finding records satisfying 10 < A < 50 ∧ 5 < B < 10?