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. Thanks in advance.

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. Volume per Ton of the Amount cargo Prot per Ton Car 0 Available tons cubic feet $ 1 4800 40 70 2 5000 35 50 3 1200 60 60 4 1700 55 80 Paul plans to solve the following optimization problem: Maximize 70 X1 + 50 X2 + 60 X3 + 80 X4 Subject to: X1 +X2 +X3 +X4 S 13,000 40 X1 + 35 X2 + 60 X3 + 55 X4 S 480,000 X1 S4800 X2 S 5000 X3 $1200 X4 $1700 X1, X2, X3, X4 2 0 Where X1, X2, X3, and X4 represent the amount (tons) to load to the ship for Cargos 1, 2, 3 and 4, respectively. A B C D E F G H 2 Linear Programmming Model 3 4 5 Decision Variables X1 X2 X3 XA 6 Number to Make 4800 5000 325 1700 7 8 9 LHS RHS 10 Constraint 1 1 1 1 11825