For the given real-world scenario, write the constraints, find the vertices of the feasible region, write the optimization equation, and find the maximum value.

A small manufacturing company makes $125 on each stereo sound bar it produces, and $100 profit on each flat screen TV it makes. Each sound bar and TV must be processed by a cutting machine (A), a fitting machine (B), and a polishing machine (C). Each sound bar must be processed on machine A for one hour, machine B for one hour, and machine C for 4 hours. Each TV must be processed on machine A for 2 hours, machine B for one hour, and on machine C for one hour. Machine A is available for 16 hours, machine B for 9, and machine C for 24 hours.