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# quot;Woody's Furniture Manufacturingquot;: An application in resource allocation Woody's Furniture Manufacturing Company produces tables and chairs....

"Woody's Furniture Manufacturing": An application in resource allocation Woody's Furniture Manufacturing Company produces tables and chairs. A table requires 8 labor hours for assembling and 2 labor hours for finishing. A chair requires 2 labor hours for assembling and 1 labor hour for finishing. The maximum number of labor hours available per day are 400 hours for assembling and 120 hours for finishing. Let x represent the number of tables produced per day, and let y represent the number of chairs produced per day. • Write a system of four linear inequalities involving x and y that, when solved, give the set of all ordered pairs (x, y) of number of tables and number of chairs that Woody's company can produce per day, given the constraints above. Next to each inequality, write a brief description of its meaning. • Carefully graph the system of linear inequalities on a separate sheet of graph paper and shade the feasible region. Is it bounded or unbounded? Identify and label on your graph the coordinates of each of the corner points. (Be sure to attach the graph when you submit your work.) • Which of the following are feasible solutions to the Woody's Furniture Manufacturing Company problem? Circle all that apply: 20 tables per day, 80 chairs per day 50 tables per day, 50 chairs per day 0 tables per day, 0 chairs per day −15 tables per day, −20 chairs per day 5 tables per day, 100 chairs per day 45 tables per day, 30 chairs per day • Finding an optimal solution: Suppose that each table produced and sold yields a $60 profit and each chair produced and sold yields a $20 profit. How many tables and chairs should Woody's company produce each day so as to maximize its daily profit? Explain your answer!