please answer a b and c and show all steps not just calculations please

a The "Pine Wood" is a firm that makes handmade dinning tables and chairs. They obtain the pine from a local tree farm, which ships them 2,500 kg of pine each month. Each table uses 50 kg of pine while each chair uses 25 kg of pine. The firm 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 "Pine Wood" $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 "Pine Wood" would like to decide how many tables and chairs to produce so as to maximize profit. A correct formulation for this problem is provided below: Let T=# of tables to produce C=# of chairs to produce Maximize P=$400T + $100C subject to (1) 507 +25C5 2,500 (2) 6T+6C 27 (4) T20, C20 1 (a) Graph the constraint lines and mark them clearly with the numbers (1), (2) and (3) to indicate which line corresponds to which constraint. Darken the feasible region. (12 points) You can NOT use a software that automatically does the plotting: you are NOT allowed to use DESMOS or any similar tool. Plotting using Excel, a paint tool or hand plotting is OK. If you wish to use a graph paper" to assist you with plotting, one is provided below (check page 4). (b) Using the graphical method, how many tables and chairs should the "Pine Wood" produce to maximize profit? What is the optimal profit? Provide all necessary steps/calculations to justify your answers. (8 points) (c) If the firm "Pine Wood" has the option to either increase the amount of Pine Wood to be shipped cach month from 2500 Kg to 2700 Kg or hire an additional part time employee that will be working 20 hours per month, which option would you recommend? Justify your answer. (3 points)