Please provide step by step solution

An Airways cargo plane has three compartments for storing cargo, namely the front, middle and rear compartments. Each of these compartments has capacity limits for weight and space, as summarized in the following table: Table 1.1 Weight and Space Limitations of each aircraft compartment Compartment Weight capacity (tons) Front 12 Center 18 Back 10 Space Capacity (m) 7005 9005 5005 In addition, the weight of the cargo in each compartment must have the same proportion with the weight capacity of the compartment, in order to maintain the balance of the aircraft. In this case, four (4) types of cargo have been planned for the delivery of the upcoming flight schedule with the following specifications: Table 1.2 Specifications for the 4 planned cargoes Cargo Weight (Tons) Volume (m/tons) Profit ($/Ton) 500 325 405 600 365 400 1 20 16 2 700 3 25 13 4 295 In this case, some combination of the proportion of cargo shipments can be made as long as it is profitable for the company. The company aims to determine how much cargo to choose for delivery and how to distribute each cargo between compartments to maximize total flight profits. a) Formulate a linear programming model for this problem! b) Solve the case model using the simplex method to find one of several optimal solutions