1- A furniture manufacturer is deciding on tables and chairs production for the upcoming quarter. Each chair sold nets the manufacturer $20; each table makes $30 in profit. The manufacture has a supply of 500 board feet each week and 100 labor hours to allocate. Each chair takes 10 board feet of wood; each table takes 20 board feet. Each chair requires 4 labor hours; each table takes 2 hours of labor. The manufacturer wants to produce no more than 40 chairs and no more than 20 tables. What should the manufacturer do? - Give the Decision Variables, constrains and the algebraic formulation of the above system, finally find the optimal solution as LP problem?