In answer to OP's original [amended here]
According to Longman Dictionary [reference needed],
"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:
why not interj informal
(expressing openness to try [sth])
