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AirMaster, a regional air cargo carrier in the Mid-West, flies a daily route between little Rock and Austin. The plane it uses has two cabins: a pressurized cabin for perishable cargo and a main cabin for containerized cargo. It charges $3000 per ton for cargo carried in the pressurized cabin; $1000 per ton for containerized cargo. The pressurized cabin has a maximum capacity of 10 tons; the containerized cabin a max capacity of 20 tons. For air safety, maximum take-off lift restriction is 28 tons and, for in-flight balance reasons, the pressurized cabin can hold, at most, 1 ton more than 2/3rds of the tonnaged carried in the main containerized cabin.
a) Formulate this problem as a standard linear programming specification.
b) Use POM to obtain the optimal solution to this problem.
c) using the "ranging" summary provided by POM, what benefit would accrue to AirMaster if the lift restriction were 30 tons instead of 28 tons?
d) As it is in this problem, what type of "bounded set" must the feasible region always form?
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