(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 2P1+P2+25P3350 Department C 4P1+4P2+4P350 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$ developed in part (b) is to be used, 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? Max25P1+27P2+29P3380y1500y2590y3 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$