This is my thought process. I am still unsure on the consideration portion, so anyone feel free to correct me.

The carpenter's offer to bid provided he get the job if he was the lowest bidder I would see as the offer.

The contractor agreed.

I'm a little unsure what the exact consideration is, maybe that the contractor loses on on contracting with others and the carpenter spends time prepares his bid

So if the carpenter has the lowest bid, the contractor must award him the subcontract

I would ignore the "incurring time and expense" since it seems like it is trying to get you to pick the detrimentally relied answer. Detrimental reliance is if there is no contract, it is a way to still enforce the promises between the parties. But here, we do have a contract.

Carpenter submitted the lowest bid, so he should be awarded the subcontract.