5.66 A food manufacturer uses an extruder (a machine that produces bite-size foods such as cookies and many snack foods) that produces revenue for the firm at the rate of $200 per hour when in operation. However, the extruder breaks down an average of two times 10 hours of operation.

If Y denotes the number of breakdowns during the time of operation, the revenue generated by the machine is given by where t denotes hours of operation. The extruder is shut down for routine maintenance on a regular schedule and operates like a new machine after this maintenance. Find the optimal maintenance interval t0 to maximize the expected revenue between shutdowns.