Problem 6 (15 points) Consider a shop floor with length and width of 200 and 100 meters respectively. There are 3 departments that need to be allocated. The following table shows the information regarding the area, the lower and upper bound of each department's length and width. Upper bound Lower bound Area Length Width Length Width Workstation 1 20 20 10 10 200 Workstation 2 45 15 30 10 450 Workstation 31 50 25 40 20 1000 The flow between the different departments is Workstation 1 Workstation 1 Workstation 1 Workstation 1 5 10 Workstation 2 10 20 Workstation 3 5 20 Develop the portions of a mathematical model (in details with numbers) as follow: 1. Develop the equation(s) to ensure that each department is within the shop floor (3 points) 2. Develop the constraint(s) to ensure there is no overlap between departments horizontally and vertically (9 points) 3. What you have to change in previous parts to ensure the model is linear? (3 points) Problem 6 (15 points) Consider a shop floor with length and width of 200 and 100 meters respectively. There are 3 departments that need to be allocated. The following table shows the information regarding the area, the lower and upper bound of each department's length and width. Upper bound Lower bound Area Length Width Length Width Workstation 1 20 20 10 10 200 Workstation 2 45 15 30 10 450 Workstation 31 50 25 40 20 1000 The flow between the different departments is Workstation 1 Workstation 1 Workstation 1 Workstation 1 5 10 Workstation 2 10 20 Workstation 3 5 20 Develop the portions of a mathematical model (in details with numbers) as follow: 1. Develop the equation(s) to ensure that each department is within the shop floor (3 points) 2. Develop the constraint(s) to ensure there is no overlap between departments horizontally and vertically (9 points) 3. What you have to change in previous parts to ensure the model is linear? (3 points)