THE TREEHUGGERS BUSINESS COMPANY makes chairs and tables from two resources $$ labor and wood. The company has $80$ hours of labor and $36$ board$-$ft$.$ of wood available each day. Demand for chairs is limited to $6$ per day. Each chair requires $8$ hours of labor and $2$ board$-$ft$.$ of wood, whereas a table requires $10$ hours of labor and $6$ board$-$ft$.$ of wood. The profit derived from each chair is $$400$ and from each table, $$100.$ The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. Solve this model by using linear programming. Questions #$1-5$: $(1)$ The final values of decision variables are: $(2)$ What is the total profit at profit$-$maximizing level of output? $(3)$ The total number of constraints in this problem, including non$-$negativity constraints is: $(4)$ The feasible region has $\_\_\_\_\_$ corner points. $(5)$ Ignoring all constraints, what is the total profit for Pinewood Furniture Company if it produces $100$ chairs and $200$ tables?