A glass factory makes two types of glass panes: a regular glass pane and a tempered glass pane. Both require time on a heating and cooling machine. Both machines are available for a maximum of 300 minutes per day. It takes 3 minutes in the heating machine and 5 minutes in the cooling machine to make one regular glass pane. It takes 5 minutes in the heating machine and 8 minutes in the cooling machine to make one tempered glass pane. The profit per pane of regular glass is $8 and the profit per pane of tempered glass is $10. How many panes of each glass type should the factory make to maximize profit? What is the maximum profit?