optimal solution without penalty and with penalty using MS Excel's Solver.

Finally, explain the differences between the two profit values. $(30$ points$)$

Company $x$ manufactures two types of clothing. The production is spearheaded by three area managers. The time requirements, profit,

and available hours in terms of area manager's availability and for each product are as follows:

All area managers want to achieve the following goals. They stated that the first two goals are equal in the top priority and the third goal

is the last priority.

Produce at least $125$ units of clothing $1$

Produce at least $80$ units of clothing $2$

Achieve a profit of at least $$300$

Furthermore, the area managers imposed the following penalties:

Product $1$: $2$ units $(+)$ and $1$ unit $(-)$

Product $2$: o unit $(-)$ and $2$ units $(+)$

Profit: $$5(-)$ and $$0(+)$