Well, a SAHM can't work outside of the home and still have the title. You would have to do your baking in their off hours, either during the night time while everyone is asleep or when they are closed for a day off like if they don't open on Mondays. So that means you'd have to pay for child care while you were at work.
To me I think you could make more constant income from just finding a job where they hold out taxes and stuff for you. It's a huge headache having to keep business accounts, pay monthly or quarterly taxes, keep track of expenses, all the little things that cost like pans, spatulas, all the tiny items that you'll have to have constant track of so that if you find yourself being audited you can produce a total package to the auditor of all the expenses and income.
This seems like a no win situation. You can't cook from home so you have to work at this profession outside of the home. So that makes you a working mom just like all the other working moms who take their kids to child care then go to work.
So if you want to work then find child care and go to work in a restaurant as their baker or stay at home and find something else. That just seems to be the better choice here.
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Now if you wanted to do a home business that was baking you might find out about renting a small space that just has a kitchen and small area around it so that you could get it inspected and do what ever you wanted to do inside those walls. You could advertise for catering and start building a name for yourself, you can sell some foods to your boyfriends associates on a trial basis. See if they sell well. This way you can also start with less costs. Rent and utilities on a very small space, just enough to qualify for an inspection....
I bet you could get some places lined up to sell your products by inviting some of the local businesses to come to a tasting session at some nice hall or local hotel conference room. They could come to a tasting and get a flier about prices then go to each section and taste the different selections with a rating scale and a blank space to put down some suggestions. Perhaps they'd like something a little more creamy or a little more tart.... They could turn that in at the end and you would have valuable information on how to tweak this business and perhaps have some contracts for edibles.
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I would also call the local health inspectors office and get the facts from the horses mouth. Talk to them about a home baking business. What modifications you'd have to make to your home.
If they say it can't be done, find out if you modified a storage building to meet the standards would that qualify. Some storage buildings at builders supply stores are quite large and they often have an upstairs that could be used as storage. If you put in a stove, a triple sink, hot water heater, and utilities would that pass a health inspection.
The good thing about this is that you could literally unplug everything and move it to another location if you ended up moving...they are solid well built buildings. I have a storage building that can be used as a garage, it has been pulled up on the back of a large truck and moved about 3 times. Still doesn't leak at all.