$2\mathrm{.}1$ CT Fumniture Company makes wooden picnic tables and chairs to sell

to various stores. These stores request both finished and unfinished

furniture. To make this furniture, CT must purchase the wood by the board

foot. It takes $25$ board feet to make one table and $10$ board feet to make

one chair. Each board foot must be purchased for $$2,$ and up to $10,000$

board feet can be purchased $.$ It takes $4$ hours to make an unfinished table

and $2$ hours to make an unfinished chair. To finish an unfinished table $($by

priming, sealing, and painting it$),$ it takes an additional $8$ hours, while it

takes $6$ hours to finish an unfinished chair. A total of $2500$ hours are

available, which can be proportioned as necessary. We can assume that all

pieces of furniture produced can be sold at the following prices: $$80$ for

unfinished table, $$120$ for finished table, $$30$ for unfinished chair, and $$55$

for a finished chair. In addition, due to typical demand, we know that, for

every table produced, at least $2$ chairs must be produced. If we have

special orders that must be filled, calling for at least $200$ tables and $450$

chairs to be sold, determine how much of each type of fumniture to produce

in order to maximize CT$\text{'}$s profit.