"Sell a range of soap bars that float so they don't get lost in the bath. One obvious way of making floaty soap - other than choosing ingredients that are less dense than water - is to add air bubbles to each bar during the manufacturing process." Would this sell well?
Well, it depends on many things.
First thing to consider - in which country it is going to be sold. Because in the UK people are trying to save water because they have to pay for it, therefore, British are more likely to take a shower instead of taking a bath. Or, according to the data I read in Cosmopolitan 3-4 years ago, French women would rather take a bath than a shower. Russians, hehe, don't pay for every litre, so we are for sure taking a bath more regular than the British people. So why British will consume much less than Russians and French.
Then competitors should be taken in account. If a famous company from the market is going to sell it, let's say 'Lush', the product would sell well. If the product is introduced by an unknown producer, then the product should be advertised very well to be able to compete with its substitutes for consumers' money.
The price is very important. The demand for this product will definately be price elastic, because a floating soap is not the thing that will be bought at a very high price level. The costs of production of this product will not be bigger than the costs of production of a usual soap, that means that the most profit will be made at the same price level with a usual soap.