How many distinct knapsack sets

Question

Knapsack Problem : Write in Canonical Form

Response to the following question:

Let

 

with a₁≥a₂≥....a_n≥0  and b≥0 . The idea is to write each such set in some simple canonical form. For example, for  ,x € B^3,

12x₁+8x₂+3x₃≤14  is equivalent to  2x₁+1x₂+1x₃≤2

(i)    When n=2, how many distinct knapsack sets are there? Write them out in a canonical form with integral coefficients and 1 =  a₁≥a₂ .

(ii)    Repeat for n = 3 with a₁≤2 .