EcoFurniture, Inc. manufactures two products made from reclaimed wood and has just received this month's allocation of $($b$)8000$ units of reclaimed wood.

It takes $3$ units of reclaimed wood to make a unit of chair $($product $1)$ and $5$ units of reclaimed wood to make a unit of table $($product $2).$

A chair generates a profit of $$70$ per unit $(p1),$ while a table generates a profit of $$200$ per unit $(p2).$

EcoFurniture has a contract calling for at least $100$ units $(m)$ of chairs this month.

The firm's facilities are such that at most $1500$ units $($u$)$ of tables may be produced monthly.

This month's production level of chairs is $1$ and tables is $2,$ respectively.

Question:

$1\mathrm{.}1)$ Write the mathematical model summary.

$1\mathrm{.}2)$ Find the optimal solution with the maximum profit $($in USD$).$