Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:

Department Product 1 Product 2 Product 3
A 3.00 2.00 1.50
B 1.00 2.50 2.00
C 0.25 0.25 0.25

During the next production period the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $28 for product 1, $30 for product 2, and $25 for product 3.

Formulate a linear programming model for maximizing total profit contribution.