Question 1: (10 points) You do have six projects under consideration, formulate an integer linear programing model to help you choose between six different projects to maximize the total payoff based on the given constraints. - You have 14 hours of labor available. - Can work on at most 3 projects. - If you work on project 4, you need to work on project 6 and vice versa. - You can work on project 3 or project 5 , but not both at the same time. Question 2: (10 points) During the war with Iraq in 1991, the Terraco Motor Company produced a lightweight, all terrain vehicle code-named " 299 Terra" for the military. The company is now planning to sell the Terra to the public. it has five plants that manufacture the vehicle and four regional distribution centers. The company is unsure of public demand for the Terra, so it is considering reducing its fixed operating costs by closing one or more plants, even though it would incur an increase in transportation costs. The relevant costs for the problein are provided in the following table. The transportation costs are per thousand vehicles shipped: for example, the cost of shipping 1.000 vehicles from plant 1 to warehouse C is $32.000. Formulate an integer programming model for this problem to assist the company in determining which plants should remain open and which should be closed and the number of vehicles that should be shipped from each plant to exch warehouse to minimize total cost. Remark only write down the model for this question. No need to find a solution or use Excel. Tix this question fas similarities with the farm/plans earrole that was covered in the classtoom