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c$.$ After evaluating the solution obtained in part $($b$),$ one of the production supervisors noted that production setup costs had not be account. She noted that setup costs are $$400$ for product $1,$$$550$ for product $2,$ and $$600$ for product $3.$ If the solution developer is to be used, what is the total profit contribution after taking into account the setup costs?

Profit $=$$

d$.$ Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommende Formulate a mixed$-$integer linear program that takes setup costs into account. Management also stated that we should not consid more than $175$ units of product $1,150$ units of product $2,$ or $140$ units of product $3.$ If required, round your answers to two decim For those boxes in which you must enter subtractive or negative numbers use a minus sign. $($Example: $-300)$ Here introduce a $0$ that is one if any quantity of product $i$ is produced and zero otherwise.