Variation on knapsack - minimum total value exceeding 'W'

Question

Given the usual n sets of items (each unlimited, say), with weights and values:

w1, v1
w2, v2
...
wn, vn

and a target weight <

Answer 1

Not too sure, but this might work. Consider the values to be the -ve of the values you have. The DP formulation would try to find max value for that weight which would be the least negative value in this case. Once you have a value, take a -ve of it for the final answer.