Find the number of American and British planes that were used to maximize cargo capacity.
On June 24, 1948, the former Soviet Union blocked all
land and water routes through East Germany to Berlin.
A gigantic airlift was organized using American and British
planes to bring food, clothing, and other supplies to the
more than 2 million people in West Berlin. The cargo
capacity was 30,000 cubic feet for an American plane and
20,000 cubic feet for a British plane. To break the Soviet
blockade, the Western Allies had to maximize cargo capacity,
but were subject to the following restrictions:
• No more than 44 planes could be used.
• The larger American planes required 16 personnel per
fight, double that of the requirement for the British
planes. The total number of personnel available could not
exceed 512.
• The cost of an American fight was $9000 and the cost of
a British fight was $5000. Total weekly costs could not
exceed $300,000.
Find the number of American and British planes that
were used to maximize cargo capacity.
With the given information, we can formulate an LPP.
Let A be number of American planes and B be number of British planes
Objective function:
Objective is to maximize the cargo.
Max 30000A + 20000B
Constraints:
(1) No more than 44 planes can be used.
A + B <= 44
(2) The larger American planes required 16 personnel per fight, double that of the requirement for the British planes. The total number of personnel available could not exceed 512.
16A + 8B <= 512
(3) The cost of an American fight was $9000 and the cost of a British fight was $5000. Total weekly costs could not exceed $300,000.
9000A + 5000B <= 300000
A,B >= 0
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