If you studied mechanical engineering and you want to start your own business, I suggest you open a garage or a car bazaar either first hand cars or second hand cars. This will be convenient for you since you have knowledge on machines and you know the best machines to use or to replace in cars. You can also sell sell car spare parts since you have knowledge on the best spare.
You have not mentioned which branch in mechanical engineering. Anyway, based on your qualification and experience, you can do some research to find out the businesses that are available for 'mechanical engineers' to start. Regarding the element of profit you may be able to know only after you start doing it.
There are numbers of business opportunity available for mechanical engineers. Most of the business in mechanical industry are in manufacturing. Here's the list of some of these businesses, you may read on.
The field of mechanical engineering creates successful enterpreneurs. There are numerous available instances. Mechanical Engineers have an advantage when it comes to establishing a strong, effective flow within their company because they are familiar with industries, manufacturing, processing, etc.
A profitable business for a mechanical engineer could be a machine design and fabrication business, a product design consultancy, a 3D printing service, or a renewable energy engineering firm.