This is the 2nd time I have had to search for starting up Zend Core automatically on Ubuntu Workstation, so here is the answer:
First change the permissions of /etc/rc.local by opening a terminal window (Applications|Accessories|Terminal) and enter the following command:
sudo chmod 777 /etc/rc.local
Then open this file with the text editor (Applications|Accessories|Text Editor) and put the following text before the exit 0 command
cd /usr/local/Zend/Core/mysql && ./bin/safe_mysqld &
/usr/local/Zend/apache2/bin/apachectl start &
Zend Core, PHP and MySQL should now all start automaticaly at boot time.