$$29$ for product $3.$

$($a$)$ Formulate a linear programming model for maximizing total profit contribution. $($Let $P_i=$ units of product i produced, for $i=1,2,3.)$

Max

s$.$t$.$

Department A

Department B

Department C

$P_1,P_2,P_{3}0$

$(P_1,P_2,P_3)=()$ with profit $$.$

$

$y_i$ be the $0-1$ 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?

Max