A carpenter makes tables and bookcases with a net unit profit of $$25$ per table and $$30$ per bookcase. He has up to $690$ board$-$ feet of lumber to devote weekly to the project and up to $120$ hr of labor. He estimates that it requires $20$ board$-$feet of lumber and $5$ hr of labor to complete a table and $30$ board$-$feet of lumber and $4$ hr of labor for a bookcase. Moreover, he has signed contracts to deliver at least four tables and two bookcases every week. The carpenter wishes to determine a weekly production schedule for tables and bookcases that maximizes his profits. Use simplex method to solve the problem.