1) Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs

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1) Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection. Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection. The profit per table is $150 while the profit per chair is $100. Currently, each week there are 300 hours of assembly time available, 220 hours of finishing time, and 30 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed 6 times the number of tables. (You may use QM-software for this problem. All the detailed output should be displayed).

a)     Formulate this as a linear programming problem. Carefully define all decision variables.

b)    Show the graph of the feasible region indicating all the relevant corner points

c)     Find the optimal solution to this LP and find the maximum profits.