This isn't necessarily a programming question just yet but is a question that many programmers at corporations might be able to answer.
My company recently switched over to Office 365. We have a "noreply" email that sends out emails whenever our customers request work. The limit for Office 365 is 30 emails per minute or 10,000 emails a day. Currently the messages are being marked as spam and will not be delivered due to these restrictions. To over come this we have heard of services like mail chimp and mail gun but by visiting their websites I wasn't able to immediately infer on how to do this.
Can anyone provide some details on how they would overcome this situation? Also is your solution one that can be applied directly to Office 365 and the email or is it something that would require code change on the server sending emails (Using SMTP to send them).
It is not possible to change this restriction in Office 365. To quote Microsoft:
"Exchange Online customers who need to send legitimate bulk commercial email (for example, customer newsletters) should use third-party providers that specialize in these services."
What you can do is use a provider like Sendgrid or any other 3'rd party SMTP relay provider.
The provider will give you an SMTP hostname that you can point your code towards as sending server. What method of authentication to use will depend on the provider.
It is important to remember that if your domain uses SPF (which is highly recommended) that you include the new providers systems in your SPF record to ensure that it is not marked as spam.