Ford produces three models of cars that are branded and sold as Mustang, Bronco and Fusion. The production process for each car includes four stages: metal frame forming, cutting, assembly, and finishing. Time available in each department to produce the cars are 630, 600, 708, and 135 hours respectively.

Each Mustang requires 0.70 hours of frame forming, 0.50 hours of cutting, 1 hour of assembly and 0.1 hours of finishing.

Each Bronco requires 1.00 hours of frame forming, 0.83 hours of cutting, 0.67 hour of assembly and 0.25 hours of finishing.

Each Fusion requires 1.00 hours of frame forming, 0.67 hours of cutting, 0.90 hour of assembly and 0.40 hours of finishing.

Revenue per car will be as follows: Mustang $250, Bronco $200, Fusion $150

Material costs per car, for the Mustang $175, for the Bronco $100, and for the Fusion $75.

The hourly labor costs for the departments are frame forming $15 per hour, cutting $12 per hour, assembly $10 per hour and finishing $10 per hour.

Write the linear programming formulation to help Ford determine the production mix of the three models that will maximize profit.