Okay, I think I've narrowed it down to two possible combinations. You're right about the possible sums being between 14 and 30.
2-8-9-10 (Sum: 29, Product: 1440)
4-6-9-10 (Sum: 29, Product: 2160)
Here's a tabular output
that shows all the combinations. I manually went through to rule out the impossible ones. But I'm stuck on narrowing it down to one solution. Hoping the OP shows up and either gives the answer or tells us whether multiple or no solutions exist. It kind of depends on Bob and the product.