Here is the simplest eye-opener that I have found in my consulting practice to convince management of the need for an open source program office:
Ask your manager to look at the open source license section under legal notices on their mobile phone. Ask them to scroll down to the end (they’ll never finish). Then point out that your product needs the same but doesn’t have it yet (if it doesn’t).
The reasoning behind this recommendation is that many managers simply don’t understand the extent to which open source is in their products. There is no better demonstration than to show them using a device they use frequently.