\$31 for product 3 . (a) Formulate a linear programming model for maximizing total profit contribution. (Let Pi= units of product i produced, for i=1, 2, 3.) max26P1+27P2+31P3 s.t. Department A 1.5P1+3P2+2P3450 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$ for product 2, and $600 for product 3 . If the solution developed in part (b) is to be used, what is the total profit contribution (in dollars) after taking into account the setup costs? $ the 01 variable that is one if any 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? Max26P1+27P2+31P3390y1550y2600y3 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 P1145y1=0 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$