List all assumptions you got directly from the question description in order to
complete (a) - (c). List and justify all additional assumptions you needed to make. I have attached the answers of (a) - (c) along with the questions. Please answer it from mathematics viewpoints correctly.

     

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1. Paul Bergey is in charge of loading cargo ships for International Cargo Company (ICC) at the port in Brisbane. Paul is preparing a loading plan for an ICC freighter destined for US. An agriculture cargos dealer wants to transport the following cargo products aboard this ship. Paul learned that this ship has space to take 480,000 cubic feet of cargo, and also has a cargo weight limit of 13,000 tons. Paul can elect to load any of the available cargos shown in the table below. Cargo 1234 4 Amount Available (tons) 4800 5000 1200 1700 Volume per Ton of the cargo (cubic feet) X₂ ≤ 5000 X3 ≤ 1200 40 35 Paul plans to solve the following optimization problem: Maximize 70 X₁ + 50 X₂ +60 X3 + 80 X4 Subject to: X4 ≤ 1700 X₁, X2, X3, X4 20 60 55 X₁ + X₂ + X3 + X4 ≤ 13,000 40 X₁ + 35 X₂ + 60 X3 + 55 X₁ ≤ 480,000 X₁ ≤ 4800 Profit per Ton (S) 70 50 60 80 Where X₁, X₁, X3, and X₁ represent the amount (tons) to load to the ship for Cargos 1, 2, 3 and 4, respectively. (a) (10 marks) Solve this Linear Programming problem in Excel using Solver and report the results. (b) (5 marks) Present a table showing how sensitive Paul's loading strategy is to the profit per ton for each type of cargo. Which cargo's profit per ton is the loading strategy most sensitive to? Why? (c) (5 marks) How much of each type of cargo should Paul accept, if the profit per ton for Cargo 1 decreases to $52? Why? 1. Paul Bergey is in charge of loading cargo ships for International Cargo Company (ICC) at the port in Brisbane. Paul is preparing a loading plan for an ICC freighter destined for US. An agriculture cargos dealer wants to transport the following cargo products aboard this ship. Paul learned that this ship has space to take 480,000 cubic feet of cargo, and also has a cargo weight limit of 13,000 tons. Paul can elect to load any of the available cargos shown in the table below. Cargo 1234 4 Amount Available (tons) 4800 5000 1200 1700 Volume per Ton of the cargo (cubic feet) X₂ ≤ 5000 X3 ≤ 1200 40 35 Paul plans to solve the following optimization problem: Maximize 70 X₁ + 50 X₂ +60 X3 + 80 X4 Subject to: X4 ≤ 1700 X₁, X2, X3, X4 20 60 55 X₁ + X₂ + X3 + X4 ≤ 13,000 40 X₁ + 35 X₂ + 60 X3 + 55 X₁ ≤ 480,000 X₁ ≤ 4800 Profit per Ton (S) 70 50 60 80 Where X₁, X₁, X3, and X₁ represent the amount (tons) to load to the ship for Cargos 1, 2, 3 and 4, respectively. (a) (10 marks) Solve this Linear Programming problem in Excel using Solver and report the results. (b) (5 marks) Present a table showing how sensitive Paul's loading strategy is to the profit per ton for each type of cargo. Which cargo's profit per ton is the loading strategy most sensitive to? Why? (c) (5 marks) How much of each type of cargo should Paul accept, if the profit per ton for Cargo 1 decreases to $52? Why?