“Woody’s Furniture Manufacturing”

Let represent the number of tables produced per day by Woody’s Furniture Manufacturing Company, and let represent the number of chairs produced per day. Write a system of four linear inequalities involving and that, when solved, give the set of all ordered pairs 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 or interpretation of its meaning.

2. Carefully graph the system of linear inequalities on a separate sheet of graph paper and then shade the feasible region. Is the bounded or unbounded? Identity and label on the graph the coordinates of each of the points. Be sure to attach the graph when you submit your work.

3. For each of the following solutions, determine whether or not it is a feasible solution to the Woody’s Furniture Manufacturing Company problem. Show your work and explain your reasoning.

(a) 20 tables per day , 80 chairs per day

(b) 50 tables per day , 50 chairs per day

(c) 0 tables per day , 0 chairs per day

(d) -15 tables per day , -20 chairs per day

(e) 5 tables per day , 100 chairs per day

(f) 45 tables per day , 30 chairs per day

4. Suppose that each table produced and sold yields a $60 profit and each chair produced and sold yields a $20 profit.

(a)