Automobile traffic from three highways, H1, H2, and H3, must stop and wait for a green light before exiting to a toll road. The tolls are 3 ,4 and 5 dollars for cars exiting from H1, H2, and H3, respectively. The flow rates from H1, H2, and H3 are 500 , 600 and 400 cars per hour. The traffic light cycle may not exceed 2.2 minutes, and the green light on any highway must be on for at least 25 seconds. The yellow light is on for 10 seconds. The toll gate can handle a maximum of 510 cars per hour. Required:
Assuming that no cars move on yellow, determine the optimal green time interval for the three highways that will maximize toll gate revenue per traffic cycle.