### Formulate this problem as linear programming

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A carpenter makes tables and chairs. Each table can be sold at the price of \$100 and each chair at the price of \$40. The carpenter works a maximum of 40 hours per week and spends 5 hours to make a table and 2 hours to make a chair. Each table needs 50 pounds of wood and 30 screws. Each chair needs 20 pounds of wood and 10 screws. Each pound of wood costs him \$0.75 and 100 screws cost him \$5. Customer demand requires that he makes at least twice as many chairs as tables. The carpenter stores the finished products in his garage, and there is room for a maximum of 9 furniture pieces each week. He should make at least 2 chairs each week. How many tables and chairs should he make to maximize his profit during a week?

Formulate this problem as a linear programming. (Write complete definition of D.V., O.F., and constraints)

Solve in Excel. (Please, print 2 spreadsheets: 1. Shows the values of the optimal solution, 2. Shows formula you use. You can see your formula by using ctrl+~).

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