Hart Manufacturing makes three products. Each product requires manufacturing operations

in three departments: A$,$ B$,$ and C$.$ The labor$-$hour requirements by the department, are as

follows:

Department Product $1$ Product $2$ Product $3$

A $1\mathrm{.}503\mathrm{.}002\mathrm{.}00$

B $2\mathrm{.}001\mathrm{.}002\mathrm{.}50$

C $0\mathrm{.}250\mathrm{.}250\mathrm{.}25$

During the next production period, the labor$-$hours available are $450$ in department A$,$

$350$ in department B$,$ and $50$ in department C$.$ The profit contributions per unit are $$25$ for

product $1,$ $$28$ for product $2,$ and $$30$ for product $3.$ One of the production supervisors

noted that production setup costs had not been taken into account. She noted that setup

costs are $$400$ for product $1,$ $$550$ for product $2,$ and $$600$ for product $3.$ Formulate a mixedinteger linear program that takes setup costs into account. Management also stated that we

should not consider making more than $175$ units of product $1,150$ units of product $2,$

or $140$ units of product $3.$ Formulate a mixed$-$integer linear program for this problem. $(4$

Marks$)$