The Pinewood Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Greensboro, North Carolina. The plant uses three main resources to make furniture$$wood$,$ upholstery, and labor. The resource requirements for each piece of furniture and the total resources available weekly are as follows:

$$ Resource Requirements

Furniture Product Wood $($lb$)$ Upholstery $($yd$)$ Labor $($hour$)$

Sofa $7129$

Table $57$

Chair $475$

Total available resources $22501000240$

The furniture is produced on a weekly basis and stored in a warehouse until the end of the week, when it is shipped out. The warehouse has a total capacity of $500$ pieces of furniture; however, a sofa takes up twice as much space as a table or chair. Each sofa earns $$320$ in profit, each table, $$275,$ and each chair, $$190.$ The company wants to know how many pieces of each type of furniture to make per week in order to maximize profit.

Formulate and solve a linear programming model for this problem.