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(a) Formulate a linear programming model for maximizing total profit contribution. (Let Pi= units of product i produced, for i=1, 2, 3.) Ma: s.t. Department A Department B Department C P1,P2,P30 (P1,P2,P3)=()withprofit$ $ $1 quantity of product i is produced and zero otherwise, for i=1,2, 3.) What is the objective function of the mixed-integer linear program? Max27P1+27P2+32P3155y1165y2170y3 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 P1155y10 Enter inequalities using less than (), less than or equal (), or greater than or equal (). units of Product 2 produced P2165y20 Enter inequalities using less than (), less than or equal (), or greater than or equal ( ). units of Product 3 produced P3170y30 Enter inequalities using less than (), less than or equal (), or greater than or equal ( ). 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)=() with profit $4350