3. (Use the graphical method for the following problem): A furniture manufac- turer makes couches and recliners. The following table gives the labor requirements and profits per piece of furniture: Couches Recliners 6 labor hours Assembly 3 labor hours $150 Design 12 labor hours 1 labor hours Profit $120 Each day, a total of 480 labor hours are available to design and 60 labor hours are available to assemble. The manufacturer wants to determine how many pieces of furniture to produce of each type in order to maximize profit. (a) Define variables for modeling this scenario and write down the objective function. (b) Identify the constraint inequalities for this problem. (c) List the corner points for the feasible region (you do not need to include a picture of your graph in your work). (d) How many couches and recliners should be produced each day to maximize profit? And, what is the maximum profit?

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