Independence Day is a national holiday and a paid holiday. Normally, organizations must remain closed on this day. However, certain essential goods and services providers and manufacturing organizations can remain open with due exemption allowed by the government. Employees required to work on such a holiday must be paid overtime at the prescribed rates or given a compensatory day off in lieu of the holiday.
However, your manufacturing concern does not appear to be producing essential goods or providing essential services to the public. Therefore, you will have to keep your factory closed. Even if you attempt to approach a competent authority for special exemption, it is too late as today is Sunday and tomorrow is the national holiday.
Regarding your request for any case law in this regard, do you believe that possessing such case law would grant you a general exemption from observing national holidays? Even if case law is provided, it may not prevent the labor inspector from penalizing your factory for violating the law, as the implications of case laws are not universal and apply only to the specific case to which they pertain.
If case laws are required for your law school exercise, as a law student aiming to be a talented lawyer, you must develop the expertise to track such legal documents yourself, as they are not readily available to serving executives.
Regards