Question: The Caspian Shipping Company runs a combined passenger/cargo jet between the Greater Odessa International Airport and Bantry, Ireland. Because of high operational expenses, the jet will not depart until all decks are properly loaded with cargo and the Captain shows up. The aircraft has three decks: lower, middle, and upper. Owing to the limited deck space, the jet cannot carry more than 100 tons of cargo for each leg of the trip. No more than 40 tons of cargo should be carried on the lower deck. For balance purposes, the middle deck must carry one third of the load of the lower deck, and the upper deck must carry two-fifths of the load of the lower deck. However, no more than 60 tons of cargo should be loaded on the middle and upper decks combined. The profit from the shipping is $8 per ton for cargo on the lower deck, $10 per ton for cargo on the middle deck, and $12 per ton for cargo on the upper deck, after all of the necessary expenses are defrayed. For mulate an LP problem to determine the highest profit loading of cargo on the various decks (i.e what quantity of cargo should be loaded on each deck to maximize profits).

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