Lots of variables:
Who owns the rights to the product when you're done? You or them? That should be a factor in the pricing, of course.
Do you have a clear spec? (If the answer is no, get one or make one.)
How confident are you in your time-estimate of 4-6 weeks? Do you feel comfortable taking the risk (i.e., doing it for a fixed price), or do you want to push the risk to them (i.e., work on it at an agreed-upon hourly rate, for however long it takes)?