3. (11 pts) A furniture manufacturer produces chairs and sofas, which are sold at prices of $160 and $140, respectively. Each sofa produced requires 6 hours of labor in the Carpentry Department of the company, and 2 hours of labor in the Upholstery Department of the company, and 1 hour in the Finishing Department. Each chair produced requires 3 hours of labor in the Carpentry Department of the company, and 6 hours of labor in the Upholstery Department of the company, and 1 hour in the Finishing Department. Each week the company has available at most 240 hours of labor in the Carpentry Department, 180 hours in the Upholstery Department, and 45 hours in the Finishing Department. How many sofas and how many chairs should the manufacturer produce each week to maximize total revenue? DO NOT actually solve this problem, instead, just set it up by answering the following a. Define all variables in the problem. (Use words.) b. What is the objective function, and should it be maximized or minimized? c. List all constraints for this problem, including the practical constraints