Chapter 4.5, Problem 20E

Use the two steps for solving a linear programming problem, given in the box on page 300, to solve the problems in Exercises 17 – 23.

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 and 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 flight, double that of the requirement for the British planes. The total number of personnel available could not exceed 512.

The cost of an American planes and the number of British flight was $ 5000. Total weekly costs could not exceed $ 300,000.

Find the number of American planes and the number of British planes that were used to maximize cargo capacity.