2. Tricky Office Furniture (TOF) produces Chairs, Desks, and Tables. Each product requires some labor hours (given in table below) in the (parts) Fabrication department, the Assembly department, and the Shipping department. For example, a chair requires 4 hours of labor in the Fabrication department, 3 hours in the Assembly department, and 2.5 hours in the Shipping department. Resource Demand (hours) Fabrication Assembly Shipping | Profit (hours) (hours) per ($) month Chairs 4 3 2.5 400 50 Product Desks 3 3 600 40 Tables 2 3.5 500 60 4 5 Demand per month of each product, and the profit per unit of each product is also given in the above table. Each department has 500 labor hours available per month. a) (16 points) Which resource is the bottleneck? What is the capacity of TOF in units per month? Fabrication: Assembly: Shipping: TOF would like to determine the optimal product mix that maximizes its profit for the month. The actual numbers of units produced of each type of product cannot exceed the demands given in the table. In addition, it requires the number of chairs produced to be at least 30% of the total number of units produced. Formulate a linear programming model to determine the optimal product mix. b) (3 points) Write the decision variables. c) (3 points) Write the objective function. d) (8 points) Write the constraints. e) (2 points) Suppose that labor force of TOF is cross-trained and all three departments can share their labor hours for whatever activities needed. How the optimization formulation would change?