Part I (linear programming model): A military submarine has three sections for storing the chemical weapons: section A, section B and section C. These sections have capacity limits on both weight and space occupation, as given below: Section A B Weight capacity (Kg) 12 18 10 Space occupation capacity (m) 7000 9000 5000 In addition, the weight of the chemical weapons in the respective sections must be the same proportion of that sections' weight capacity to keep the balance of the military submarine. The following four shifts have been required for the shipment of the weapons on an upcoming trip as space is available: Shifts 1 2 3 4 Weight (Kg) 20 16 25 13 Volume (m/kg) 500 700 600 400 Profit (S/Kg) 280 360 320 250 Furthermore, any portion of these shifts can be allowed. The Submarine captain needs your help to decide how much of each shift should be allowed and how the distribution of the weapons would be among the submarine sections to maximize the total profits of the upcoming trip. You are required to: a) Identify the decision variables clearly. b) Formulate a linear programming model for this problem. c) Construct the dual problem of the linear programing model. d) Solve the LP using a software package of your choice to find an optimal solution to maximize the profit (Software package: Matlab or Excel solver). Part I (linear programming model): A military submarine has three sections for storing the chemical weapons: section A, section B and section C. These sections have capacity limits on both weight and space occupation, as given below: Section A B Weight capacity (Kg) 12 18 10 Space occupation capacity (m) 7000 9000 5000 In addition, the weight of the chemical weapons in the respective sections must be the same proportion of that sections' weight capacity to keep the balance of the military submarine. The following four shifts have been required for the shipment of the weapons on an upcoming trip as space is available: Shifts 1 2 3 4 Weight (Kg) 20 16 25 13 Volume (m/kg) 500 700 600 400 Profit (S/Kg) 280 360 320 250 Furthermore, any portion of these shifts can be allowed. The Submarine captain needs your help to decide how much of each shift should be allowed and how the distribution of the weapons would be among the submarine sections to maximize the total profits of the upcoming trip. You are required to: a) Identify the decision variables clearly. b) Formulate a linear programming model for this problem. c) Construct the dual problem of the linear programing model. d) Solve the LP using a software package of your choice to find an optimal solution to maximize the profit (Software package: Matlab or Excel solver)