In answer to OP's original

According to Longman Dictionary, 

*"Why not" is a "spoken phrase" used to say that you agree with a suggestion.*

My question is: Can I use *Why not?* in 'formal writing' as in the following sentence:

We then thought we might investigate whether an increase in the temperature resulted in a better yield. Why not?



According to Wordreference.com: 
**Principal Translation**
**why not** *interj*	*informal* (expressing openness to try [sth])

**Compound Forms**
**Why not?** *expr*	(why is that not so?)