Hart Manufacturing

After evaluating the solution obtained in part $($b$),$ one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $$370$ for product $1,$ $$540$ for product $2,$ and $$610$ 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?

Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part $($b$).$ Formulate a mixed$-$integer linear program that takes setup costs into account. Management also stated that we should not consider making more than $150$ units of product $1,155$ units of product $2,$ or $160$ units of product $3.($Let

Pi $=$units of product i produced and yi

be the $0-1$ variable that is one if any quantity of product i is produced and zero otherwise, for

i $=1,2,3.)$