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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 1.50 3.00 2.00 B 2.00 1.00 2.50 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 $26 for product 1, $28 for product 2, and $31 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution (in $). (Let P = units of product i produced, for i = 1, 2, 3.) Max s.t. Department A Department B Department C Pa, P2, P320 (b) Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution (in dollars)? (P, P2, P3) = with profit $1