Producing a bookshelf requires $8$ boards and $6$ screws. Producing a TV stand requires $6$ boards and $18$ screws. Each bookshelf yields $$25$ profit, and each TV stand yields $$20$ profit. There are $120$ boards and $198$ screws available. Sketch the feasible region. How many bookshelves and TV stands need to be sold to realize the maximum profit? What is the maximum profit?

Eight bookshelves and $9$ TV stands for a maximum profit of $$380$

Nine bookshelves and $8TV$ stands for a maximum profit of $$385$

$15$ bookshelves and $11TV$ stands for a maximum profit of $$595$