Solution 1 - using an Apex trigger

Because this requirement means that many child records (opportunities) need to be updated when a parent record (Account) is edited, we can't achieve the preceding business requirement using the Workflow rule. The next possibility is to use an Apex trigger. Generally, a developer writes an Apex trigger on the Account object to update all the open opportunities when an account's custom field, out of business, gets updated to True. The following is the sample code:

trigger UpdateRelatedOpportunites on Account (after update) { 
for (Account AccountToUpdate : trigger.new)
{
If (AccountToUpdate.Out_Of_Business__c==True)
{
// Your logic;
}
}
}

In addition, you'll need a test class and then use a change set, Force.com IDE or Force.com Migration Tool, to deploy the trigger and test classes to production. This also means that any change to the business logic will require more development work.