For each of the problems provide the formulated optimization model and its optimal solution and value.

$2\mathrm{.}1$ CT Furniture 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 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 furniture to produce