A furniture company manufactures tables and chairs. A table requires 40 board feet of wood, and a chair requires 30 board feet of wood. Wood can be purchased at a cost of $1.50 per board foot, and 40,000 board feet of wood are available for purchase. It takes two hours of skilled labor to manufacture an unfinished table or an unfinished chair. Three more hours of skilled labor will turn an unfinished table into a finished table, and two more hours of skilled labor will turn an unfinished chair into a finished chair. A total of 5,000 hours of skilled labor is available (and have already been paid for). All furniture produced can be sold at the following unit prices: an unfinished table, $130; a finished table, $220; an unfinished chair, $80; a finished chair, $175.

a)Define the decision variables and write down the detailed mathematical formulation of the company's optimization problem to maximize its total profit.

b Solve the optimization problem by Excel Solver. Write down the company's detailed optimal decisions and optimal profit.