$(10$ marks$)$ A simple home garage door is to be controlled by PLC$.$ When a car parks in front of the garage door and on top of the proximity sensor the garage door opens after $8$ seconds. A motor rotates moves in the UP direction and opens the garage door. An upper limit sensor at the top of the door stops the garage door. When the car moves in$,$ the garage door closes after $10$ seconds. The motor moves in the DOWN direction until it is stopped by the lower limit sensor$.$ A red light is on when the motor is moving in the UP or Down direction and green when the motor is not moving. Develop a ladder diagram to control the garage door. In this ladder diagram one contact $($coil$)$ is used for the UP Motor and another one for Down Motor.