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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. (a) Formulate a linear programming model for maximizing total profit contribution. (Let Pi= units of product i produced, for i=1,2,3.) Max s.t. Department A Department B Department C P1,P2,P30 (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)? (P1,P2,P3)=()withprofit$ what is the total profit contribution (in dollars) after taking into account the setup costs? $ What is the objective function of the mixed-integer linear program? Max In addition to the constraints from part (a), what other constraints should be added to the mixed-integer linear program? s.t. units of Product 1 produced units of Product 2 produced units of Product 3 produced P1,P2,P30;y1,y2,y3=0,1 (e) Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit (in dollars) contribution? (P1,P2,P3,y1,y2,y3)=()withprofit$