How to make unit economics work for cheap items?

I have a unique idea for a body wash but I tried to model the unit economics and see what my profit would be, and it looks like it would be negative. Can you help see if my assumptions are right?

Selling price: $15 (pretty standard)

Returns (10%): – $1.5

Referral Fee (15%): -$2.25

FBA Fees: -$3.7

Closing Fee: -$1

Product Cost: -$2 (probably a little less)

PPC (33%): -$5

Gross Profit: -$0.45

The returns fee might be a little high and same for the product cost and PPC if you factor in repeat orders, but still…best case scenario I earn $4 or so on each FBA order. This product can maybe make sense off of Amazon but on Amazon it seems competitive and has a bad gross profit. Are my assumptions right? Should I ditch the idea? I see many companies like Lume (a new-ish company) have done really well on Amazon, so I’m wondering if I’m missing something or if they just make most of their sales off of Amazon?