Reference no: EM133234920

The container ships sent from the San Francisco pier need to be carefully balanced in order to sail correctly to the markets beyond the Pacific Ocean. Usually, these ships have three storage places: back, center, and front, each of them with different weight and volume capacities. The back can carry up to 2,000 tons or 100,000 m3 of products. The center can carry up to 3,000 tons or 135,000 m3. The front can carry up to 1,500 tons or 30,000 m3.

A particular ship is going to be loaded with three particular products (i.e., cars, computers, and home appliances). There are 4,000 tons of cars, 6,000 tons of computers, and 2,000 tons of home appliances ready to be shipped. Each ton of car occupies 50 m3, while each ton of computers occupies 60 m3, and each ton of home appliances occupies 25 m3 of volume. It costs $600 to transport each ton of car, but the ship charges $1,400 per ton to the car producer. Similarly, it costs $1,000 to transport a ton of computers, while the producer is charged with $1,600 per ton. Finally, transporting a ton of home appliances costs $750, and the ship charges $1,200 per ton transported to the producer. To ensure a quick delivery without any complications in the ocean, the [weight/weight ca-pacity] ratio must be the same for all the storage places.

1. Formulate a mathematical model for this problem utilizing the six-step process.

2. Perform a sensitivity analysis and indicate which area of the ship do you recommend to increase its weight or volume capacity and why. Then, increase its maximum allowance and compare the results with the ones obtained in part 2.