$2\mathrm{.}19.$ The Oak Works is a family$-$owned business that makes handcrafted dining room tables and chairs. They obtain the oak from a local tree farm, which ships them $2,500$ pounds of oak each month. Each table uses $50$ pounds of oak while each chair uses $25$ pounds of oak. The family builds all the furniture itself and has $480$ hours of labor available each month. Each table or chair requires six hours of labor. Each table nets Oak Works $$400$ in profit, while each chair nets $$100$ in profit. Since chairs are often sold with the tables, they want to produce at least twice as many chairs as tables.

The Oak Works would like to decide how many tables and chairs to produce so as to maximize profit.

a$.$ Formulate and solve a linear programming model for this problem on a spreadsheet by using the Excel Solver.

AS b$.$ Use Analytic Solver to formulate and solve this model in a spreadsheet.

c$.$ Formulate this same model algebraically.