Reference no: EM133898073
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.
Amount
Volume per Ton of the
cargo Profit per Ton
Cargo 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 ????1 + 50 ????2 + 60 ????3 + 80 ????4
Subject to:
????1 + ????2 + ????3 + ????4 ≤ 13,000
40 ????1 + 35 ????2 + 60 ????3 + 55 ????4 ≤ 480,000
????1 ≤ 4800
????2 ≤ 5000
????3 ≤ 1200
????4 ≤ 1700
????1, ????2, ????3, ????4 ≥ 0
Where ????1, ????2, ????3, and ????4 represent the amount (tons) to load to the ship for Cargos 1, 2, 3 and 4, respectively.
1. Solve this Linear Programming problem in Excel using Solver and report the results.
2. 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?
3. How much of each type of cargo should Paul accept, if the profit per ton for Cargo 1 decreases to $52? Why?
4. Now, the dealer makes further requirement about loading the ship: if a type of cargo is to be shipped, at least 500 tons of that type need to be shipped; otherwise, that type of cargo should not be shipped at all.
5. How much of each type of cargo to accept, in order to maximize the profit? Please describe how you will model this problem differently from (a), and report the result. Be specific in your answer.