$1.$ LO $\backslash (1=20\backslash \%\backslash )($a$),$ LO $\backslash (2=20\backslash \%\backslash )($b$)$

The Alea Company sells two models of its patented three$-$leg tables. The basic version uses a wood top, requires $2$ hours to assemble, and sells for a profit of $\backslash (\backslash$$ $305\backslash ).$ The deluxe model takes $2\mathrm{.}5$ hours to assemble $($because of its glass top$)$ and sells for a profit of $\backslash (\backslash$$ $480\backslash ).$ Over the next week, the company will have $300$ legs, $60$ wood tops, $40$ glass tops, and $80$ hours of assembly available.

Question:

a$.$ Determine step by step the mathematical formulation based on the problem $($manual and using software$).$

b$.$ Determine a maximum profit production plan assuming that everything produced can be sold and give a recommendation for the Planning Department.