Because this is an external application, you want to send keystrokes
(specifically Tabs and Enter commands) to the external program.

AS A LAST RESORT (according to my resident expert programmer Peter G), you can
use SendKeys from VBA.

Issue with special characters is that you need to enclose them in curly
brackets, or something like that. E.g. Sendkeys({Tab}) - don't quote me.

Lastly, since the message  box is from an external program, VBA will not know
when it appears. So now you have to synchronise time (which in your application
should be easy to do - Start solver, wait for 5.5 minutes, then send
keystrokes), and then repeat.

If SendKeys does not do it for you, perhaps search on Google Newsgroups for
"Sendkeys Alternative".

We did this a few years a go with SendKeys and an external model, and it was
messy.