In the beer serving problem, you are given a set of beer brands with the number of bottles you have of each beer; a set of guests each with a number of bottles of beer they wish to drink, and which beer brands thay find acceptable. Guests are willing to mix different types of beers, as long as each beer is acceptable to them. You want to know how to satisfy each guest, if possible. Design and analyze a polynomial algorithm to solve this problem.

Suppose there is a relation r(a, b, c) with a b+-tree index with search keys (a, b).1. what is the worst-case cost of finding records satisfying 10 < a < 50 using this index, in terms of the number of records n1, retrieved and the height h of the tree? 2. what is the worst-case cost of finding records satisfying 10 < a < 50 and 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? 3. under what conditions on n1 and n2, would the index be an efficient way of finding records satisfying the condition from part (2)?