Polynomial reduction from unbounded knapsack problem to general integer programming
Hint: What do you know about the complexity class of the unbounded knapsack problem?  Is it in P?  Is it NP-hard?

Now what do you know about the complexity class of LP?  Is it in NP?

Think a bit about your answers to those two questions and see if that helps you see one path forward.  (There's a short proof of your desired result that doesn't require much detailed mathematics.)



Once you've figured that out:  if I told you that I was giving you an oracle for some NP-complete problem, what other problems could you use it to solve (in polynomial time)? (Possible hint: Take a look at the definition of NP-complete and think about what the implications of that are...)



Once you've worked out that: you should now know there is a reduction. So look at the proofs of each of the steps of reasoning I walked you through. Review these proofs. Those proofs will construct a reduction for you. So, work out what reduction is implicit in the proofs. You should be able to take it from here!