Linear programming problem

4. (15 points) Automobile traffic from three highways, H1, H2, and H3, must stop and wait for a green light before exiting to the toll road (all three highways exit to the same toll road at the same traffic light point). The tolls are $3, $4, and $5 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 at least 25 seconds. The yellow light is on for 10 seconds. The toll gate can handle a maximum of 510 cars per hour. Assuming no cars move on yellow, formulate a linear program that will determine the optimal green time interval for the three highways that will maximize toll gate revenue per traffic cycle