Joes Furniture, LLC$,$ manufactures both press wood bookshelves and desks. Management wants to develop a linear programming model to determine the numbers of bookshelves and desks to better utilize the labor resources. The contributions to fixed cost and profit each bookshelf and each desk are $$11$ and $$13,$ respectively. The following table gives labor requirements in the Cutting, Drilling and Packaging departments, as well as the total number of labor hours available in each department per day.